Finite $p$-groups with minimum number of central automorphisms fixing the center element-wise

TL;DR

This paper characterizes finite p-groups of order up to p^7 where the group of central automorphisms fixing the center element-wise is minimized, providing insights into their automorphism structure.

Contribution

It offers a classification of small finite p-groups based on the minimality of their central automorphism groups fixing the center.

Findings

Identifies all such p-groups of order up to p^7

Determines the structure of their automorphism groups

Provides criteria for minimality of central automorphisms

Abstract

We characterize finite $p$-groups $G$ of order up to $p^7$ for which the group of central automorphisms fixing the center element-wise is of minimum possibe order.