A note on automorphisms of finite p-groups

S. Mohsen Ghoraishi


Let $p$ be an odd prime and let $G$ be a finite $p$-group such that $xZ(G)\subseteq x^G$, for all $x \in G - Z(G)$ where
$x^G$ denotes the conjugacy class of $x$ in $G$. Then $G$ has a non-inner automorphism of order $p$ leaving the
Frattini subgroup $\Phi(G)$ element-wise fixed.

DOI: 10.1017/S0004972712000214


Finite p-groups, Automorphisms of p-groups, Non-inner automorphisms, Camina pairs.

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