Centralizers of automorphisms permuting free generators

By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the f...
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Autor*in:	Macedońska Olga [verfasserIn] Tomaszewski Witold [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	permutation centralizer automorphism 20e05 20e36 20f28

Übergeordnetes Werk:	In: Open Mathematics - De Gruyter, 2015, 17(2019), 1, Seite 15-22
Übergeordnetes Werk:	volume:17 ; year:2019 ; number:1 ; pages:15-22

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/math-2019-0007

Katalog-ID:	DOAJ060189843

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520			\|a By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm).
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allfields	10.1515/math-2019-0007 doi (DE-627)DOAJ060189843 (DE-599)DOAJc8331db628794c7f87075e08910f3ff4 DE-627 ger DE-627 rakwb eng QA1-939 Macedońska Olga verfasserin aut Centralizers of automorphisms permuting free generators 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm). permutation centralizer automorphism 20e05 20e36 20f28 Mathematics Tomaszewski Witold verfasserin aut In Open Mathematics De Gruyter, 2015 17(2019), 1, Seite 15-22 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:17 year:2019 number:1 pages:15-22 https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 kostenfrei https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 17 2019 1 15-22
spelling	10.1515/math-2019-0007 doi (DE-627)DOAJ060189843 (DE-599)DOAJc8331db628794c7f87075e08910f3ff4 DE-627 ger DE-627 rakwb eng QA1-939 Macedońska Olga verfasserin aut Centralizers of automorphisms permuting free generators 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm). permutation centralizer automorphism 20e05 20e36 20f28 Mathematics Tomaszewski Witold verfasserin aut In Open Mathematics De Gruyter, 2015 17(2019), 1, Seite 15-22 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:17 year:2019 number:1 pages:15-22 https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 kostenfrei https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 17 2019 1 15-22
allfields_unstemmed	10.1515/math-2019-0007 doi (DE-627)DOAJ060189843 (DE-599)DOAJc8331db628794c7f87075e08910f3ff4 DE-627 ger DE-627 rakwb eng QA1-939 Macedońska Olga verfasserin aut Centralizers of automorphisms permuting free generators 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm). permutation centralizer automorphism 20e05 20e36 20f28 Mathematics Tomaszewski Witold verfasserin aut In Open Mathematics De Gruyter, 2015 17(2019), 1, Seite 15-22 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:17 year:2019 number:1 pages:15-22 https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 kostenfrei https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 17 2019 1 15-22
allfieldsGer	10.1515/math-2019-0007 doi (DE-627)DOAJ060189843 (DE-599)DOAJc8331db628794c7f87075e08910f3ff4 DE-627 ger DE-627 rakwb eng QA1-939 Macedońska Olga verfasserin aut Centralizers of automorphisms permuting free generators 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm). permutation centralizer automorphism 20e05 20e36 20f28 Mathematics Tomaszewski Witold verfasserin aut In Open Mathematics De Gruyter, 2015 17(2019), 1, Seite 15-22 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:17 year:2019 number:1 pages:15-22 https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 kostenfrei https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 17 2019 1 15-22
allfieldsSound	10.1515/math-2019-0007 doi (DE-627)DOAJ060189843 (DE-599)DOAJc8331db628794c7f87075e08910f3ff4 DE-627 ger DE-627 rakwb eng QA1-939 Macedońska Olga verfasserin aut Centralizers of automorphisms permuting free generators 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm). permutation centralizer automorphism 20e05 20e36 20f28 Mathematics Tomaszewski Witold verfasserin aut In Open Mathematics De Gruyter, 2015 17(2019), 1, Seite 15-22 (DE-627)823698734 (DE-600)2818690-4 23915455 nnns volume:17 year:2019 number:1 pages:15-22 https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 kostenfrei https://doi.org/10.1515/math-2019-0007 kostenfrei https://doaj.org/toc/2391-5455 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 17 2019 1 15-22
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callnumber-first	Q - Science
author	Macedońska Olga
spellingShingle	Macedońska Olga misc QA1-939 misc permutation misc centralizer misc automorphism misc 20e05 misc 20e36 misc 20f28 misc Mathematics Centralizers of automorphisms permuting free generators
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topic_title	QA1-939 Centralizers of automorphisms permuting free generators permutation centralizer automorphism 20e05 20e36 20f28
topic	misc QA1-939 misc permutation misc centralizer misc automorphism misc 20e05 misc 20e36 misc 20f28 misc Mathematics
topic_unstemmed	misc QA1-939 misc permutation misc centralizer misc automorphism misc 20e05 misc 20e36 misc 20f28 misc Mathematics
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title	Centralizers of automorphisms permuting free generators
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title_full	Centralizers of automorphisms permuting free generators
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title_sort	centralizers of automorphisms permuting free generators
callnumber	QA1-939
title_auth	Centralizers of automorphisms permuting free generators
abstract	By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm).
abstractGer	By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm).
abstract_unstemmed	By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm. It is known that the centralizer of the permutation σ in Skm is isomorphic to a wreath product Zk ≀ Sm and is generated by its two subgroups: the first one is isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$, the direct product of m cyclic groups of order k, and the second one is Sm. We show that the centralizer of the automorphism σ ∈ Aut(Fkm) is generated by its subgroups isomorphic to Zkm$\begin{array}{} \displaystyle Z_k^m \end{array}$ and Aut(Fm).
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title_short	Centralizers of automorphisms permuting free generators
url	https://doi.org/10.1515/math-2019-0007 https://doaj.org/article/c8331db628794c7f87075e08910f3ff4 https://doaj.org/toc/2391-5455
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