On the Order of the Schur Multiplier of a Pair of Finite p-Groups

TL;DR

This paper characterizes the structure of pairs of finite p-groups based on the order of their Schur multiplier, providing insights into their algebraic properties under certain conditions.

Contribution

It offers a new characterization of finite p-group pairs using the order of their Schur multiplier, advancing understanding of their structural properties.

Findings

Provides conditions under which the structure of (G,N) is determined by the order of M(G,N)

Establishes a relationship between the order of the Schur multiplier and the properties of p-groups

Enhances tools for analyzing pairs of finite p-groups in group theory

Abstract

In 1998, G. Ellis defined the Schur multiplier of a pair $(G,N)$ of groups and mentioned that this notion is a useful tool for studying pairs of groups. In this paper, we characterize the structure of a pair of finite $p$-groups $(G,N)$ in terms of the order of the Schur multiplier of $(G,N)$ under some conditions.