Finite p-groups with central automorphism group of minimal order

TL;DR

This paper investigates finite p-groups with coclass up to 4 that have the smallest possible central automorphism groups, providing simplified proofs of existing key results.

Contribution

It characterizes finite p-groups with minimal central automorphism groups and offers elementary proofs of known theorems in this area.

Findings

Identification of p-groups with minimal Aut_z(G) for coclass up to 4

Simplified proofs of Sharma and Gumber's main results

Characterization of automorphism groups in specific p-groups

Abstract

We study finite p-groups G of coclass upto 4 for which the group Aut_z(G) of all central automorphisms of G is of minimal possible order. As a consequence, we obtain very short and elementary proofs of main results of Sharma and Gumber [7].