A remark on the capability of finite $p$-groups

TL;DR

This paper classifies specific finite p-groups based on their capability, derived subgroup order, and quotient rank, providing a detailed understanding of their structure.

Contribution

It offers a complete classification of capable finite p-groups with a derived subgroup of order p and a quotient of rank n-1.

Findings

Classification of capable finite p-groups under given conditions

Structural insights into the derived subgroup and quotient group

Extension of known results in p-group theory

Abstract

In this paper we classify all capable finite $p$-groups with derived subgroup of order $p$ and $G/G'$ of rank $n-1$.