Description of Barely Transitive Groups with Soluble Point Stabilizer

Betin, Cansu
Kuzucuoğlu, Mahmut
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.
Communications in Algebra


On the condensation property of the lamplighter groups and groups of intermediate growth
Benli, Mustafa Gökhan (Lugansk Taras Shevchenko National University, 2014-06-01)
The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group L = Z2 ≀ Z is a condensation group and has a minimal presentation by generators and relators. The condensation property is achieved by showing that L belongs to a Cantor subset of the space M2 of marked 2-generated groups consisting mostly of groups of intermediate growth.
On locally graded barely transitive groups
Betin, Cansu; Kuzucuoğlu, Mahmut (2013-07-01)
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.
About the decomposability of almost completely decomposable groups
Budak, Canan; Solak, Ebru; Department of Mathematics (2020-8)
Almost completely decomposable groups are extensions of completely decomposable groups of finite index. They can be written as a sum of indecomposables. Every almost completely decomposable group is the direct sum of indecomposables but this decomposition is quite complicated and not unique. Almost completely decomposable groups can be represented by matrices, called coordinate matrices. If the coordinate matrix of a given almost completely decomposable group is decomposable then the group is decomposable. ...
Universal groups of intermediate growth and their invariant random subgroups
Benli, Mustafa Gökhan; Nagnibeda, Tatiana (2015-07-01)
We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.
Locally finite groups and their subgroups with small centralizers
ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut; Shunwatsky, Pavel (2017-07-01)
Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): An infinite simple locally finite group G admits an elementary abelian p-group of automorphisms A such that C-G(A) is Chernikov and C-G(A) Keywords: involves no inf...
Citation Formats
C. Betin and M. Kuzucuoğlu, “Description of Barely Transitive Groups with Soluble Point Stabilizer,” Communications in Algebra, pp. 1901–1907, 2009, Accessed: 00, 2020. [Online]. Available: