A M\"obius function on the centralizer lattice

TL;DR

This paper investigates the M"obius function within the poset of element centers in p-groups, providing new insights into the structure of centralizers.

Contribution

It introduces novel results about the M"obius function on the centralizer lattice in p-groups, expanding understanding of their algebraic structure.

Findings

Derived new formulas for the M"obius function on centralizer posets.

Enhanced understanding of the structure of centralizers in p-groups.

Provided theoretical tools for analyzing subgroup lattices.

Abstract

We consider the M\"obius function on the poset of element centers and obtain some new results regarding centralizers in a $p$-group.