A group G is called a barely transitive group if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup is finite.
A subgroup H of a group G is called a permutable subgroup, if H commutes with every subgroup of G. We showed that if an infinitely generated barely transitive group G has a permutable point stabilizer, then G is locally finite.
We proved that if a barely transitive group G has an abelian point stabilizer H, then G is isomorphic to one of the followings:
(i) G is a metabelian locally finite p-group,
(ii) G is a finitely generated quasi-finite group (in particular H is finite),
(iii) G is a finitely generated group with a maximal normal subgroup N where N is a locally finite metabelian group. In particular, G=N is a quasi-finite simple group.
In all of the three cases, G is periodic.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12608605/index.pdf |
| Date | 01 June 2007 |
| Creators | Betin, Cansu |
| Contributors | Kuzucuoglu, Mahmut |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
Page generated in 0.0016 seconds