De Falco, Maria
De Giovanni, Francesco
Kuzucuoğlu, Mahmut
Musella, Carmela
A group G is said to have the AFC-property if for each element x of G at least one of the indices vertical bar G : C-G (x)vertical bar and vertical bar C-G (x) : x vertical bar is finite. The class of AFC-groups, which generalize FC-groups, has been studied by De Falco et al. (2017) and Shalev (1994). Here the structure of groups whose proper subgroups have the AFC-property is investigated.


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.
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...
Groups of automorphisms with TNI-centralizers
Ercan, Gülin (2018-03-15)
A subgroup H of a finite group G is called a TNI-subgroup if N-G(H) boolean AND H-9 = 1 for any g is an element of G \ N-G (H). Let A be a group acting on G by automorphisms where C-G(A) is a TNI-subgroup of G. We prove that G is solvable if and only if C-G(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of C-G(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed point...
The mapping class group is generated by two commutators
Baykur, R. Inanc; Korkmaz, Mustafa (2021-05-01)
We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators. (C) 2021 Elsevier Inc. All rights reserved.
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
M. De Falco, F. De Giovanni, M. Kuzucuoğlu, and C. Musella, “GROUPS WHOSE PROPER SUBGROUPS HAVE RESTRICTED INFINITE CONJUGACY CLASSES,” COLLOQUIUM MATHEMATICUM, pp. 281–291, 2017, Accessed: 00, 2020. [Online]. Available: