# A Theorem of Frobenius and Its Applications

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

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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