The non-commutative Specker phenomenon in the uncountable case
| dc.creator | Eda, Katsuya | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-11-27 | |
| dc.date.accessioned | 2026-07-07T04:38:52Z | |
| dc.date.available | 2026-07-07T04:38:52Z | |
| dc.description | An infinitary version of the notion of free products has been introduced and investigated by G.Higman. Let G_i (for i in I) be groups and ast_{i in X} G_i the free product of G_i (i in X) for X Subset I and p_{XY}: ast_{i in Y} G_{i}->ast_{i in X} G_{i} the canonical homomorphism for X subseteq Y Subset I. (X Subset I denotes that X is a finite subset of I.) Then, the unrestricted free product is the inverse limit lim (ast_{i in X} G_i, p_{XY}: X subseteq Y Subset I). We remark ast_{i in emptyset} G_i= {e} . We prove: Theorem: Let F be a free group. Then, for each homomorphism h:lim ast G_i-> F there exist countably complete ultrafilters u_0,...,u_m on I such that h = h . p_{U_0 cup ... cup U_m} for every U_0 in u_0, ...,U_m in u_m. If the cardinality of the index set I is less than the least measurable cardinal, then there exists a finite subset X_0 of I and a homomorphism overline {h}: ast_{i in X_0}G_i-> F such that h= overline {h} . p_{X_0}, where p_{X_0}: lim ast G_i->ast_{i in X_0}G_i is the canonical projection. | |
| dc.identifier | https://arxiv.org/abs/math/0011231 | |
| dc.identifier | http://arxiv.org/abs/math/0011231 | |
| dc.identifier | J. Algebra 252 No. 1 (2002) 22--26 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60449 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | The non-commutative Specker phenomenon in the uncountable case | |
| dc.type | text |