Frobenius' result on simple groups of order (p^3-p)/2
Group Theory
2011-07-22 v1 History and Overview
Abstract
The complete list of pairs of non-isomorphic finite simple groups having the same order is well-known. In particular for p>3, PSL_2(Z/p) is the "only" simple group of order (p^3-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 PSL_2(Z/p) is simple for p>3; a result stated by Galois in 1832.
Cite
@article{arxiv.1107.4130,
title = {Frobenius' result on simple groups of order (p^3-p)/2},
author = {Paul Monsky},
journal= {arXiv preprint arXiv:1107.4130},
year = {2011}
}
Comments
10 pages