Non-inner automorphisms of order $p$ in finite $p$-groups of coclass $4$ and $5$

Author(s):

Patali Komma *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
A long-standing conjecture asserts that every finite nonabelian $p$-group has a non-inner automorphism of order $p$. This paper proves the conjecture for finite $p$-groups of coclass $4$ and $5$ ($p\ge 5$). We also prove the conjecture for an odd order nonabelian $p$-group $G$ with cyclic center satisfying $C_G(G^p\gamma_3(G))\cap Z_3(G)\le Z(\Phi(G))$.
Keywords:

finite $p$-groups , Non-inner automorphisms , Coclass

Language:
English
Published:
International Journal of Group Theory, Volume:13 Issue: 1, Mar 2024
Pages:
97 to 114
https://www.magiran.com/p2662258