On local finiteness of periodic residually finite groups

Download

index.pdf

Date

2002-10-01

Author

Kuzucouoglu, M
Shumyatsky, P

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

188
views

0
downloads

Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.

Subject Keywords

Automorphisms, Centralizers, Periodic groups

URI

https://hdl.handle.net/11511/65296

Journal

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1017/s0013091501000311

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS Ercan, Gülin; Ogut, Elif (2014-01-01) We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
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...
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
Centralizers of involutions in locally finite-simple groups Berkman, A.; Kuzucuoğlu, Mahmut; OeZyurt, E. (2007-01-01) We consider infinite locally finite-simple groups (that is, infinite groups in which every finite subset lies in a finite simple subgroup). We first prove that in such groups, centralizers of involutions either are soluble or involve an infinite simple group, and we conclude that in either case centralizers of involutions are not inert subgroups. We also show that in such groups, the centralizer of an involution is linear if and only if the ambient group is linear.
Prime graphs of solvable groups Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8) If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.

Citation Formats

M. Kuzucouoglu and P. Shumyatsky, “On local finiteness of periodic residually finite groups,” PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, pp. 717–721, 2002, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65296.