Finite simple groups and localization
Copyright policy )Finite simple groups and localization
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.
17 pages. See also http://magma.unil.ch/jscherer/ The two last sections (especially that about preservation of simplicity by localizations) have been removed and will be the subject of a separate paper. Some proofs have been rewritten in a clearer style
- University of Almería Spain
- University of Lausanne Switzerland
inclusions, rigid components, Group Theory (math.GR), Simple groups, localizations, Automorphisms of infinite groups, exceptional groups of Lie type, finite simple groups, FOS: Mathematics, Algebraic Topology (math.AT), group homomorphisms, sporadic groups, Simple groups: alternating groups and groups of Lie type, Mathematics - Algebraic Topology, alternating groups, Mathematics - Group Theory, Simple groups: sporadic groups
inclusions, rigid components, Group Theory (math.GR), Simple groups, localizations, Automorphisms of infinite groups, exceptional groups of Lie type, finite simple groups, FOS: Mathematics, Algebraic Topology (math.AT), group homomorphisms, sporadic groups, Simple groups: alternating groups and groups of Lie type, Mathematics - Algebraic Topology, alternating groups, Mathematics - Group Theory, Simple groups: sporadic groups
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