A note on automorphisms of finite $p$-groups
Gustavo A. Fern\'andez-Alcober, Anitha Thillaisundaram

TL;DR
This paper investigates conditions under which the order of a finite non-cyclic p-group divides the order of its automorphism group, focusing on groups with specific abelian or elementary abelian substructures.
Contribution
It establishes new divisibility conditions for automorphism groups of certain finite p-groups based on their subgroup structures.
Findings
If G has an abelian maximal subgroup, then |G| divides |Aut(G)|.
If G has an elementary abelian center with C_G(Z(Φ(G))) ≠ Φ(G), then |G| divides |Aut(G)|.
Abstract
Let be a finite non-cyclic -group of order at least . If has an abelian maximal subgroup, or if has an elementary abelian centre with , then divides .
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Taxonomy
TopicsFinite Group Theory Research · Japanese History and Culture · graph theory and CDMA systems
