Philip Hall's Problem On Non-Abelian Splitters
| dc.creator | Göbel, Rüdiger | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-09-08 | |
| dc.date.accessioned | 2026-07-07T04:37:18Z | |
| dc.date.available | 2026-07-07T04:37:18Z | |
| dc.description | Philip Hall raised around 1965 the following question which is stated in the Kourovka Notebook: Is there a non-trivial group which is isomorphic with every proper extension of itself by itself? We will decompose the problem into two parts: We want to find non-commutative splitters, that are groups G not= 1 with Ext(G,G)=1 . The class of splitters fortunately is quite large so that extra properties can be added to G. We can consider groups G with the following properties: There is a complete group L with cartesian product L^omega cong G, Hom(L^omega,S_omega)=0 (S_omega the infinite symmetric group acting on omega) and End(L,L)=Inn(L) cup {0}. We will show that these properties ensure that G is a splitter and hence obviously a Hall-group in the above sense. Then we will apply a recent result from our joint paper math.GR/0009089 which also shows that such groups exist, in fact there is a class of Hall-groups which is not a set. | |
| dc.identifier | https://arxiv.org/abs/math/0009091 | |
| dc.identifier | http://arxiv.org/abs/math/0009091 | |
| dc.identifier | Math. Proc. Cambridge Philos. Soc. 134 No. 1 (2003) 23--31 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59900 | |
| dc.subject | Group Theory | |
| dc.subject | Logic | |
| dc.subject | Rings and Algebras | |
| dc.title | Philip Hall's Problem On Non-Abelian Splitters | |
| dc.type | text |