# Congruence condition on number of abelian subgroups of order eight and exponent dividing four

From Groupprops

This article is about a congruence condition.

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## Contents

## Statement

### Statement in terms of universal congruence condition

The collection of abelian groups of order and exponent dividing is a Collection of groups satisfying a universal congruence condition (?) for the prime .

### Hands-on statement

Suppose is a finite p-group where . In other words, the order of is a power of . Then, if has an abelian subgroup of order and exponent dividing , the number of abelian subgroups of of order and exponent dividing is congruent to modulo .

## Related facts

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