# Congruence condition on number of subgroups of given prime power order and bounded exponent in abelian group

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This article is about a congruence condition.

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## Statement

Let be a prime number and suppose is an abelian group of prime power order, i.e., a finite -group. Suppose is a power of less than or equal to the order of and is a power of less than or equal to .

Then, the number of subgroups of of order and exponent dividing is either equal to zero or congruent to modulo .