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...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2013-12-01
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| Series: | International Journal of Group Theory |
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| Online Access: | http://www.theoryofgroups.ir/?_action=showPDF&article=2761&_ob=dbf6c7e37f884c3d7c270219cb030012&fileName=full_text.pdf. |
| _version_ | 1818096716932448256 |
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| author | Alireza Abdollahi S. Mohsen Ghoraishi |
| author_facet | Alireza Abdollahi S. Mohsen Ghoraishi |
| author_sort | Alireza Abdollahi |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-10T23:09:03Z |
| format | Article |
| id | doaj.art-4a644caff9ac4aa587324cf75dbad3ca |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-10T23:09:03Z |
| publishDate | 2013-12-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-4a644caff9ac4aa587324cf75dbad3ca2022-12-22T01:30:00ZengUniversity 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 |
| 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 |
| title | 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_short | Noninner automorphisms of finite p-groups leaving the center elementwise fixed |
| title_sort | noninner automorphisms of finite p groups leaving the center 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. |
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