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EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER p IN SOME FINITE p-GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 September 2012

M. SHABANI-ATTAR
M. SHABANI-ATTAR*
Affiliation:
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran (email: mehdishabani9@yahoo.com, m_shabaniattar@pnu.ac.ir)
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Abstract

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Let G be a nonabelian finite p-group of order pm. A long-standing conjecture asserts that G admits a noninner automorphism of order p. In this paper we prove the validity of the conjecture if exp (G)=pm−2. We also show that if G is a finite p-group of maximal class, then G has at least p(p−1) noninner automorphisms of order p which fix Φ(G) elementwise.

Keywords

noninner automorphisms of order pp-groups

MSC classification

Secondary: 20D45: Automorphisms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 272 - 277
Copyright
©2012 Australian Mathematical Publishing Association Inc.

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