Large localizations of finite simple groups
| dc.creator | Goebel, Ruediger | |
| dc.creator | Rodriguez, Jose L. | |
| dc.creator | Shelah, Saharon | |
| dc.date | 1999-12-22 | |
| dc.date.accessioned | 2026-07-07T05:32:27Z | |
| dc.date.available | 2026-07-07T05:32:27Z | |
| dc.description | A group homomorphism eta:H-->G is called a localization of H if every homomorphism phi:H-->G can be `extended uniquely' to a homomorphism Phi:G-->G in the sense that Phi eta=phi. Libman showed that a localization of a finite group need not be finite. This is exemplified by a well-known representation A_n-->SO_{n-1}(R) of the alternating group A_n, which turns out to be a localization for n even and n>9. Dror Farjoun asked if there is any upper bound in cardinality for localizations of A_n. In this paper we answer this question and prove, under the generalized continuum hypothesis, that every non abelian finite simple group H, has arbitrarily large localizations. This shows that there is a proper class of distinct homotopy types which are localizations of a given Eilenberg--Mac Lane space K(H,1) for any non abelian finite simple group H. | |
| dc.identifier | https://arxiv.org/abs/math/9912191 | |
| dc.identifier | http://arxiv.org/abs/math/9912191 | |
| dc.identifier | Shelah [GRSh:701] | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79662 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.title | Large localizations of finite simple groups | |
| dc.type | text |