A Remark on the Number of Maximal Abelian Subgroups

TL;DR

This paper proves that in finite p-groups, the count of maximal abelian subgroups always leaves a remainder of 1 when divided by p, revealing a specific modular property.

Contribution

It establishes a new congruence relation for the number of maximal abelian subgroups in finite p-groups, enhancing understanding of their subgroup structure.

Findings

Number of maximal abelian subgroups ≡ 1 (mod p)

Provides a modular property of subgroup counts in finite p-groups

Advances subgroup enumeration theory in finite group analysis

Abstract

The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.