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arXiv · 1107.4130

Frobenius' result on simple groups of order (p^3-p)/2

Paul Monsky
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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.

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Paul Monsky. 2011-07-20. Frobenius' result on simple groups of order (p^3-p)/2. https://arxiv.org/abs/1107.4130

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