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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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