A note on non-inner automorphism conjecture

P. Komma

Published 2021-03-15Version 1

In this paper we prove that for $p\ge 5$, every $2$-generator finite $p$-group $G$ has a non-inner automorphism of order $p$ leaving $G^p\gamma_4(G)$ elementwise fixed. As a consequence we have the same result for finite $p$-groups of coclass $4$ and coclass $5$ for $p\ge 5$.