Noninner automorphisms of finite p-groups leaving the center elementwise fixed

Noninner automorphisms of finite p-groups leaving the center elementwise fixed

A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner au...

Full description

Bibliographic Details
Main Authors: Alireza Abdollahi, S. Mohsen Ghoraishi
Format: Article
Language:English
Published: University of Isfahan 2013-12-01
Series:International Journal of Group Theory
Subjects:
Noninner automorphism
finite p-groups
the center
Online Access:http://www.theoryofgroups.ir/?_action=showPDF&article=2761&_ob=dbf6c7e37f884c3d7c270219cb030012&fileName=full_text.pdf.
id doaj-4a644caff9ac4aa587324cf75dbad3ca
record_format Article
spelling doaj-4a644caff9ac4aa587324cf75dbad3ca2020-11-25T02:26:51ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692013-12-01241720Noninner automorphisms of finite p-groups leaving the center elementwise fixedAlireza AbdollahiS. Mohsen GhoraishiA longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner automorphism of order p leaving either the center Z(G) or the Frattini subgroup Phi(G) of G elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves Z(G) elementwise fixed.http://www.theoryofgroups.ir/?_action=showPDF&article=2761&_ob=dbf6c7e37f884c3d7c270219cb030012&fileName=full_text.pdf.Noninner automorphismfinite p-groupsthe center
collection DOAJ
language English
format Article
sources DOAJ
author Alireza Abdollahi
S. Mohsen Ghoraishi
spellingShingle Alireza Abdollahi
S. Mohsen Ghoraishi
Noninner automorphisms of finite p-groups leaving the center elementwise fixed
International Journal of Group Theory
Noninner automorphism
finite p-groups
the center
author_facet Alireza Abdollahi
S. Mohsen Ghoraishi
author_sort Alireza Abdollahi
title Noninner automorphisms of finite p-groups leaving the center elementwise fixed
title_short Noninner automorphisms of finite p-groups leaving the center elementwise fixed
title_full Noninner automorphisms of finite p-groups leaving the center elementwise fixed
title_fullStr Noninner automorphisms of finite p-groups leaving the center elementwise fixed
title_full_unstemmed Noninner automorphisms of finite p-groups leaving the center elementwise fixed
title_sort noninner automorphisms of finite p-groups leaving the center elementwise fixed
publisher University of Isfahan
series International Journal of Group Theory
issn 2251-7650
2251-7669
publishDate 2013-12-01
description A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner automorphism of order p leaving either the center Z(G) or the Frattini subgroup Phi(G) of G elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves Z(G) elementwise fixed.
topic Noninner automorphism
finite p-groups
the center
url http://www.theoryofgroups.ir/?_action=showPDF&article=2761&_ob=dbf6c7e37f884c3d7c270219cb030012&fileName=full_text.pdf.
work_keys_str_mv AT alirezaabdollahi noninnerautomorphismsoffinitepgroupsleavingthecenterelementwisefixed
AT smohsenghoraishi noninnerautomorphismsoffinitepgroupsleavingthecenterelementwisefixed
_version_ 1724845359738388480

Similar Items