The failure of the uncountable non-commutative Specker Phenomenon
| dc.creator | Shelah, Saharon | |
| dc.creator | Strüngmann, Lutz | |
| dc.date | 2000-09-05 | |
| dc.date.accessioned | 2026-07-07T04:37:11Z | |
| dc.date.available | 2026-07-07T04:37:11Z | |
| dc.description | Higman proved in 1952 that every free group is non-commutatively slender, this is to say that if G is a free group and h is a homomorphism from the countable complete free product (X_omega Z) to G, then there exists a finite subset F of omega and a homomorphism h:*_{i in F} Z --> G such that h=h rho_F, where rho_F is the natural map from (X_{i in omega})Z to *_{i in F}Z . Corresponding to the abelian case this phenomenon was called the non-commutative Specker Phenomenon. In this paper we show that Higman's result fails if one passes from countable to uncountable. In particular, we show that for non-trivial groups G_alpha (alpha in lambda) and uncountable cardinal lambda there are 2^{2^lambda} homomorphisms from the complete free product of the G_alpha 's to the ring of integers. | |
| dc.identifier | https://arxiv.org/abs/math/0009045 | |
| dc.identifier | http://arxiv.org/abs/math/0009045 | |
| dc.identifier | J. Group Theory 4 No. 4 (2001) 417--426 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59864 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.subject | 20E06 | |
| dc.title | The failure of the uncountable non-commutative Specker Phenomenon | |
| dc.type | text |