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ON p-AUTOMORPHISMS THAT ARE INNER

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 June 2009

M. SHABANI ATTAR
M. SHABANI ATTAR*
Affiliation:
Faculty of Science, Department of Mathematics, University of Payam Noor, Mashad, 91735-433, Iran (email: mehdishabani9@yahoo.com, m_shabaniattar@pnu.ac.ir)
*
✉For correspondence; e-mail: mehdishabani9@yahoo.com,m_shabaniattar@pnu.ac.ir
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Abstract

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Let G be a group and let CAutΦ(G)(Z(Φ(G))) be the set of all automorphisms of G centralizing G/Φ(G) and Z(Φ(G)). For each prime p and finite p-group G, we prove that CAutΦ(G)(Z(Φ(G)))≤Inn(G) if and only if G is elementary abelian or Φ(G)=Z(G) and Z(G) is cyclic.

Keywords

automorphismcentral automorphismfinite p-group

MSC classification

Secondary: 20D45: Automorphisms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 291 - 293
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

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