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EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER p IN SOME FINITE p-GROUPS
Published online by Cambridge University Press: 17 September 2012
Abstract
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.
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- Research Article
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- ©2012 Australian Mathematical Publishing Association Inc.
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