On locally graded barely transitive groups

Betin, Cansu
Kuzucuoğlu, Mahmut
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.


On the existence of kappa-existentially closed groups
Kegel, Otto H.; Kaya, Burak; Kuzucuoğlu, Mahmut (2018-09-01)
We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinalityκ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists noκ-existentially closed group of cardinality κ for singular κ. Assuming thegeneralized continuum hypothesis, we completely determine the cardinalsκ ≤ λ for which a κ-existentially closed group of cardinality λ exists
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...
Description of Barely Transitive Groups with Soluble Point Stabilizer
Betin, Cansu; Kuzucuoğlu, Mahmut (Informa UK Limited, 2009-6-4)
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.
The Influence of some embedding properties of subgroups on the structure of a finite group
Kızmaz, Muhammet Yasir; Ercan, Gülin; Department of Mathematics (2018)
In a finite group $G$, a subgroup $H$ is called a $TI$-subgroup if $H$ intersects trivially with distinct conjugates of itself. Suppose that $H$ is a Hall $pi$-subgroup of $G$ which is also a $TI$-subgroup. A famous theorem of Frobenius states that $G$ has a normal $pi$-complement whenever $H$ is self normalizing. In this case, $H$ is called a Frobenius complement and $G$ is said to be a Frobenius group. A first main result in this thesis is the following generalization of Frobenius' Theorem. textbf{Theorem...
Rank and Order of a Finite Group Admitting a Frobenius-Like Group of Automorphisms
Ercan, Gülin; Khukhro, E. I. (2014-07-01)
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either |FH| is odd or |H| = 2). In the case where G is a finite p-group such that G = [G, F] it is proved that the rank of G is bounded ab...
Citation Formats
C. Betin and M. Kuzucuoğlu, “On locally graded barely transitive groups,” CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, pp. 1188–1196, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38465.