Finite $p$-groups of class 2 have noninner automorphisms of order $p$

Details Finite $p$-groups of class 2 have noninner automorphisms of order $p$ Finite $p$-groups of class 2 have noninner automorphisms of order $p$

2006-08-23

arxiv.org/abs/math/0608581v1

Mathematics

Group Theory

6 pages. to appear in Journal of Algebra

Scientific paper

We prove that for any prime number $p$, every finite non-abelian $p$-group
$G$ of class 2 has a noninner automorphism of order $p$ leaving either the
Frattini subgroup $\Phi(G)$ or $\Omega_1(Z(G))$ elementwise fixed.

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