DESCRIPTION OF BARELY TRANSITIVE GROUPS WITH SOLUBLE POINT STABILIZER

Betin C., KUZUCUOĞLU M.

COMMUNICATIONS IN ALGEBRA, vol.37, no.6, pp.1901-1907, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 6
  • Publication Date: 2009
  • Doi Number: 10.1080/00927870802210076
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1901-1907
  • Keywords: Locally finite groups, Permutable subgroup, Quasi finite groups, INFINITE GROUPS, SUBGROUPS
  • Middle East Technical University Affiliated: Yes

Abstract

We describe the barely transitive groups with abelian-by-finite, nilpotent-by-finite and soluble-by-finite point stabilizer. In article [6] Hartley asked whether there is a torsionfree barely transitive group. One consequence of our results is that there is no torsionfree barely transitive group whose point stabilizer is nilpotent. Moreover, we show that if the stabilizer of a point is a permutable subgroup of an infinitely generated barely transitive group G, then G is locally finite.