000130456 001__ 130456
000130456 005__ 20190316234441.0
000130456 0247_ $$2doi$$a10.1007/BF02785857
000130456 037__ $$aARTICLE
000130456 245__ $$aFinite simple groups and localization
000130456 269__ $$a2002
000130456 260__ $$c2002
000130456 336__ $$aJournal Articles
000130456 520__ $$aThe 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. In some cases, we also consider automorphism groups and universal covering groups and we show that a localization of a finite simple group may not be simple.
000130456 6531_ $$alocalizations
000130456 6531_ $$a group homomorphisms
000130456 6531_ $$a finite simple groups
000130456 6531_ $$a rigid 	components
000130456 6531_ $$a alternating groups
000130456 6531_ $$a sporadic groups
000130456 6531_ $$a inclusions
000130456 6531_ $$a 	exceptional groups of Lie type
000130456 700__ $$aRodríguez, José L.
000130456 700__ $$aScherer, Jérôme
000130456 700__ $$g123676$$aThévenaz, Jacques$$0243565
000130456 773__ $$j131$$tIsrael Journal of Mathematics$$q185-202
000130456 8564_ $$zURL
000130456 8564_ $$zURL
000130456 8564_ $$uhttps://infoscience.epfl.ch/record/130456/files/localization.ps$$zn/a$$s257224
000130456 909C0 $$xU10861$$0252233$$pCTG
000130456 909CO $$ooai:infoscience.tind.io:130456$$qGLOBAL_SET$$qSB$$particle
000130456 937__ $$aCTG-ARTICLE-2002-001
000130456 970__ $$a1010.20007/CTG
000130456 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000130456 980__ $$aARTICLE