On locally graded barely transitive groups


Betin C., KUZUCUOĞLU M.

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, vol.11, no.7, pp.1188-1196, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 7
  • Publication Date: 2013
  • Doi Number: 10.2478/s11533-013-0240-x
  • Journal Name: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1188-1196
  • Middle East Technical University Affiliated: Yes

Abstract

We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup aOE (c) x > which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H (1) of finite index in H satisfying the identity chi(H (1)) = 1, where chi is a multi-linear commutator of weight w.