Finite π-groups with normal injectors
Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal F...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Vorob’ev, N. T. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Siberian mathematical journal - Pleiades Publishing, 1966, 56(2015), 4 vom: Juli, Seite 624-630 |
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| Übergeordnetes Werk: |
volume:56 ; year:2015 ; number:4 ; month:07 ; pages:624-630 |
| Links: |
|---|
| DOI / URN: |
10.1134/S0037446615040060 |
|---|
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OLC2033389111 |
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| 520 | |a Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. | ||
| 650 | 4 | |a Fitting class | |
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10.1134/S0037446615040060 doi (DE-627)OLC2033389111 (DE-He213)S0037446615040060-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes Martsinkevich, A. V. aut Enthalten in Siberian mathematical journal Pleiades Publishing, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 56 2015 4 07 624-630 |
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10.1134/S0037446615040060 doi (DE-627)OLC2033389111 (DE-He213)S0037446615040060-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes Martsinkevich, A. V. aut Enthalten in Siberian mathematical journal Pleiades Publishing, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 56 2015 4 07 624-630 |
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10.1134/S0037446615040060 doi (DE-627)OLC2033389111 (DE-He213)S0037446615040060-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes Martsinkevich, A. V. aut Enthalten in Siberian mathematical journal Pleiades Publishing, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 56 2015 4 07 624-630 |
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10.1134/S0037446615040060 doi (DE-627)OLC2033389111 (DE-He213)S0037446615040060-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes Martsinkevich, A. V. aut Enthalten in Siberian mathematical journal Pleiades Publishing, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 56 2015 4 07 624-630 |
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10.1134/S0037446615040060 doi (DE-627)OLC2033389111 (DE-He213)S0037446615040060-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes Martsinkevich, A. V. aut Enthalten in Siberian mathematical journal Pleiades Publishing, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 56 2015 4 07 624-630 |
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Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. © Pleiades Publishing, Ltd. 2015 |
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Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. © Pleiades Publishing, Ltd. 2015 |
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Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. © Pleiades Publishing, Ltd. 2015 |
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2024-07-03T16:47:54.183Z |
| _version_ |
1803577221905907712 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2033389111</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504044152.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2015 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0037446615040060</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2033389111</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S0037446615040060-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Vorob’ev, N. T.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Finite π-groups with normal injectors</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fitting class</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">π-normal Fitting class</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">product of Fitting classes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">lattice join of Fitting classes</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Martsinkevich, A. V.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Siberian mathematical journal</subfield><subfield code="d">Pleiades Publishing, 1966</subfield><subfield code="g">56(2015), 4 vom: Juli, Seite 624-630</subfield><subfield code="w">(DE-627)129553573</subfield><subfield code="w">(DE-600)220062-4</subfield><subfield code="w">(DE-576)015009602</subfield><subfield code="x">0037-4466</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:56</subfield><subfield code="g">year:2015</subfield><subfield code="g">number:4</subfield><subfield code="g">month:07</subfield><subfield code="g">pages:624-630</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S0037446615040060</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">56</subfield><subfield code="j">2015</subfield><subfield code="e">4</subfield><subfield code="c">07</subfield><subfield code="h">624-630</subfield></datafield></record></collection>
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