Variants of theorems of Baer and Hall on finite-by-hypercentral groups
We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is...
Ausführliche Beschreibung
Gespeichert in:
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Casolo, Carlo [verfasserIn] |
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Umfang: |
9 |
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| Übergeordnetes Werk: |
Enthalten in: A two stage successive estimation based maximum power point tracking technique for photovoltaic modules - Christy Mano Raj, J.S. ELSEVIER, 2014, San Diego, Calif |
|---|---|
| Übergeordnetes Werk: |
volume:452 ; year:2016 ; day:15 ; month:04 ; pages:279-287 ; extent:9 |
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10.1016/j.jalgebra.2015.12.023 |
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| 520 | |a We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is finite. This completes recent results generalizing classical theorems by R. Baer and P. Hall. Then we extend other results in the literature by applying our results to groups of automorphisms acting in a restricted way on an ascending normal series of a group G. | ||
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10.1016/j.jalgebra.2015.12.023 doi GBVA2016022000030.pica (DE-627)ELV035625058 (ELSEVIER)S0021-8693(16)00022-3 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 333.7 610 VZ 44.13 bkl Casolo, Carlo verfasserin aut Variants of theorems of Baer and Hall on finite-by-hypercentral groups 2016 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is finite. This completes recent results generalizing classical theorems by R. Baer and P. Hall. Then we extend other results in the literature by applying our results to groups of automorphisms acting in a restricted way on an ascending normal series of a group G. secondary Elsevier 20F28 Elsevier primary Elsevier Dardano, Ulderico oth Rinauro, Silvana oth Enthalten in Elsevier Christy Mano Raj, J.S. ELSEVIER A two stage successive estimation based maximum power point tracking technique for photovoltaic modules 2014 San Diego, Calif (DE-627)ELV018117414 volume:452 year:2016 day:15 month:04 pages:279-287 extent:9 https://doi.org/10.1016/j.jalgebra.2015.12.023 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 GBV_ILN_2532 44.13 Medizinische Ökologie VZ AR 452 2016 15 0415 279-287 9 045F 510 |
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We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is finite. This completes recent results generalizing classical theorems by R. Baer and P. Hall. Then we extend other results in the literature by applying our results to groups of automorphisms acting in a restricted way on an ascending normal series of a group G. |
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We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is finite. This completes recent results generalizing classical theorems by R. Baer and P. Hall. Then we extend other results in the literature by applying our results to groups of automorphisms acting in a restricted way on an ascending normal series of a group G. |
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We show that if a group G has a finite normal subgroup L such that G / L is hypercentral, then the index of the (upper) hypercenter of G is at most | Aut ( L ) | ⋅ | L | . It follows an explicit bound for | G / Z 2 m ( G ) | in terms of d = | γ m + 1 ( G ) | and independent of m ∈ N , provided d is finite. This completes recent results generalizing classical theorems by R. Baer and P. Hall. Then we extend other results in the literature by applying our results to groups of automorphisms acting in a restricted way on an ascending normal series of a group G. |
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