A 5-local identification of the Monster. (Q1764453)

This paper provides a characterization of the Monster sporadic simple group in terms of its 5-local structure. Under the general hypothesis that every composition factor of every local subgroup of \(G\) is a known simple group, it is shown that if \(G\) is a finite group with a Sylow 5-subgroup having centre \(Z\) of order 5, and \(N_G(Z)\) is of shape \(5^{1+6}4J_2.2\), then subject to the non-triviality conditions that \(4J_2.2\) acts faithfully on \(Q\cong 5^{1+6}\) and that \(Q\) contains more than one \(G\)-conjugate of \(Z\), in fact \(G\) is the Monster. The context of this work is the classification of groups of `local characteristic \(p\)', where many of the ideas from the Classification of Finite Simple Groups are generalized from the prime 2 to arbitrary primes \(p\).