Frobenius' result on simple groups of order (p³-p)/2

2011/07/20 by Paul Monsky, Monsky, Paul
Engineering · Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #History and Overview (math.HO) #graph theory and CDMA systems #math.GR #math.HO

paper · pdf · doi:10.48550/arxiv.1107.4130

10 pages

arxiv created 2011/07/20 · openalex publication_date 2011/07/20 · arxiv updated 2011/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The complete list of pairs of non-isomorphic finite simple groups having the same order is well-known. In particular for p>3, PSL₂(Z/p) is the "only" simple group of order (p³-p)/2. It's less well-known that Frobenius proved this uniqueness result in 1902. This note presents a version of Frobenius' argument that might be used in an undergraduate honors algebra course. It also includes a short modern proof, aimed at the same audience, of the much earlier result that PSL₂(Z/p) is simple for p>3; a result stated by Galois in 1832.

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