Normal Automorphisms of Free Burnside Groups of Period 3

If any normal subgroup of a group $G$ is $\phi$-invariant for some automorphism $\phi$ of $G$, then $\phi$ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group $B(m,3...

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Main Authors:	Varujan Atabekyan, H.T. Aslanyan, A. E. Grigoryan
Format:	Article
Language:	English
Published:	Republic of Armenia National Academy of Sciences 2017-12-01
Series:	Armenian Journal of Mathematics
Subjects:	normal automorphism, inner automorphism, periodic group, free Burnside group, free group
Online Access:	http://armjmath.sci.am/index.php/ajm/article/view/157

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spelling	doaj-e068cf0d288a442bb4448ce02396bf152020-11-25T00:11:36ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632017-12-0192Normal Automorphisms of Free Burnside Groups of Period 3Varujan Atabekyan0H.T. Aslanyan1A. E. Grigoryan2Head of Chair Algebra and Geometry, Yerevan State UniversityRussian-Armenian University, 123 Hovsep Emin str. 0051 Yerevan, ArmeniaRussian-Armenian University, 123 Hovsep Emin str. 0051 Yerevan, Armenia If any normal subgroup of a group $G$ is $\phi$-invariant for some automorphism $\phi$ of $G$, then $\phi$ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group $B(m,3)$ of period 3 is inner for all rank $m\ge3$. http://armjmath.sci.am/index.php/ajm/article/view/157normal automorphism, inner automorphism, periodic group, free Burnside group, free group
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Varujan Atabekyan H.T. Aslanyan A. E. Grigoryan
spellingShingle	Varujan Atabekyan H.T. Aslanyan A. E. Grigoryan Normal Automorphisms of Free Burnside Groups of Period 3 Armenian Journal of Mathematics normal automorphism, inner automorphism, periodic group, free Burnside group, free group
author_facet	Varujan Atabekyan H.T. Aslanyan A. E. Grigoryan
author_sort	Varujan Atabekyan
title	Normal Automorphisms of Free Burnside Groups of Period 3
title_short	Normal Automorphisms of Free Burnside Groups of Period 3
title_full	Normal Automorphisms of Free Burnside Groups of Period 3
title_fullStr	Normal Automorphisms of Free Burnside Groups of Period 3
title_full_unstemmed	Normal Automorphisms of Free Burnside Groups of Period 3
title_sort	normal automorphisms of free burnside groups of period 3
publisher	Republic of Armenia National Academy of Sciences
series	Armenian Journal of Mathematics
issn	1829-1163
publishDate	2017-12-01
description	If any normal subgroup of a group $G$ is $\phi$-invariant for some automorphism $\phi$ of $G$, then $\phi$ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group $B(m,3)$ of period 3 is inner for all rank $m\ge3$.
topic	normal automorphism, inner automorphism, periodic group, free Burnside group, free group
url	http://armjmath.sci.am/index.php/ajm/article/view/157
work_keys_str_mv	AT varujanatabekyan normalautomorphismsoffreeburnsidegroupsofperiod3 AT htaslanyan normalautomorphismsoffreeburnsidegroupsofperiod3 AT aegrigoryan normalautomorphismsoffreeburnsidegroupsofperiod3
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Normal Automorphisms of Free Burnside Groups of Period 3

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