# A Theorem of Frobenius and Its Applications

by Anjana Khurana (Punjabi University) and Dinesh Khurana (Punjabi University)

This article originally appeared in:
Mathematics Magazine
June, 2005

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Groups
Applicable Course(s): 4.2 Mod Algebra I & II

The Frobenius Theorem states that if $$d$$ is a divisor of the order of a finite group $$G$$, then the number of solutions of $$x^d = 1$$ in $$G$$ is a multiple of $$d$$. The article includes a proof and applications of the theorem.

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