A Combinatorial Proof of a generalization of a Theorem of Frobenius

Abstract

In this article, we shall generalize a theorem due to Frobenius in group theory, which asserts that if $p$ is a prime and $p^r$ divides the order of a finite group, then the number of subgroups of order $p^r$ is $\equiv$ 1(mod $p$). Interestingly, our proof is purely combinatorial and does not use much group theory.

Accepted for publication in "The Mathematics Student" Journal