The Automorphism Group of p-Central p-Groups

TL;DR

This paper investigates the automorphism groups of p-central p-groups, establishing that for certain finite p-central p-groups, the group's order divides the order of its automorphism group, revealing structural properties.

Contribution

It proves that for a subset of finite p-central p-groups, the order of the group divides the order of its automorphism group, a new divisibility property.

Findings

Order of G divides order of Aut(G) for certain p-central p-groups

Structural insights into automorphism groups of p-central p-groups

Extension of known automorphism group properties to p-central groups

Abstract

A p-group G is p-central if the central quotient has exponent p. We prove that for a subset of finite p-central p-groups, the order of the group G divides the order of Aut(G).