Pseudocentralizers and the Chermak Delgado Measure of the Mod $p^{n}$ Heisenberg Group

TL;DR

This paper computes the Chermak-Delgado measure for the mod p^n Heisenberg group by introducing the pseudocentralizer, providing new insights into its structure and properties.

Contribution

It introduces the concept of pseudocentralizer and applies it to determine the Chermak-Delgado measure of the mod p^n Heisenberg group, a novel approach in this area.

Findings

Computed the Chermak-Delgado measure for the mod p^n Heisenberg group.

Introduced and analyzed the properties of pseudocentralizers.

Provided new structural insights into the group's measure and centralizer relations.

Abstract

In this paper we compute the Chermak-Delgado measure of the mod $p^{n}$ Heisenberg Group for any prime $p$. To achieve this we introduce the notion of the pseudocentralizer and prove various results about it.