Finite simple groups and localization

Details Finite simple groups and localization Finite simple groups and localization

2000-12-21

arxiv.org/abs/math/0012217v2

Mathematics

Group Theory

17 pages. See also http://magma.unil.ch/jscherer/ The two last sections (especially that about preservation of simplicity by l

Scientific paper

The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup and we apply it in various cases. Iterating this process allows us to connect many simple groups by a sequence of localizations. We prove that all sporadic simple groups (except possibly the Monster) and several groups of Lie type are connected to alternating groups. The question remains open whether or not there are several connected components within the family of finite simple groups.

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