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Mahmut Kuzucuoğlu

E-mail
matmah@metu.edu.tr
Department
Department of Mathematics
Scopus Author ID
Normalizers of finite subgroups in homogenous symmetric groups and automorphisms
Guven, Ulviye Bursra; Kuzucuoğlu, Mahmut (Informa UK Limited, 2019-05-21)
The structure of the centralizers of finite subgroups in homogenous symmetric groups S(chi(xi)) are given up to isomorphism by Guven-Kegel-Kuzucuoglu in 2015 and Kuzucuoglu-Oliynyk-Sushchansky in 2018. In this article, we ...
On the existence of kappa-existentially closed groups
Kaya, Burak; Kegel, Otto H.; 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 cardinality κ fo...
kappa-Existentially closed groups
Kegel, Otto H.; Kuzucuoğlu, Mahmut (2018-04-01)
Let kappa is be an infinite cardinal. The class of kappa-existentially closed groups is defined and their basic properties are studied. Moreover, for an uncountable cardinal kappa, uniqueness of kappa-existentially closed ...
Homogeneous monomial groups and centralizers
Kuzucuoğlu, Mahmut; Oliynyk, Bogdana; Sushchanskyy, Vitaly I. (2018-01-01)
The construction of homogeneous monomial groups are given and their basic properties are studied. The structure of a centralizer of an element is completely described and the problem of conjugacy of two elements is resolve...
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...
Centralizers of finite subgroups in Hall's universal group
Kegel, Otto H.; Kuzucuoğlu, Mahmut (2017-01-01)
The structure of the centralizers of elements and finite abelian subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall's universal group in the class of ...
Centralizers of Finite p-Subgroups in Simple Locally Finite Groups
Kuzucuoğlu, Mahmut (Siberian Federal University, 2017-01-01)
We are interested in the following questions of B. Hartley: (1) Is it true that, in an infinite, simple locally finite group, if the centralizer of a finite subgroup is linear, then G is linear? (2) For a finite subgroup F...
GROUPS WHOSE PROPER SUBGROUPS HAVE RESTRICTED INFINITE CONJUGACY CLASSES
De Falco, Maria; De Giovanni, Francesco; Kuzucuoğlu, Mahmut; Musella, Carmela (2017-01-01)
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 ge...
HOMOGENOUS FINITARY SYMMETRIC GROUPS
Kegel, Otto. H.; Kuzucuoğlu, Mahmut (2015-03-01)
We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let n be an infinite cardinal. If G = boolean OR(infinity)(i...
CENTRALIZERS OF SUBGROUPS IN DIRECT LIMITS OF SYMMETRIC GROUPS WITH STRICTLY DIAGONAL EMBEDDING
Guven, U. B.; Kegel, O. H.; Kuzucuoğlu, Mahmut (2015-01-01)
Let =(p(1), p(2),...) be a given infinite sequence of not necessarily distinct primes. In 1976, the structure of locally finite groups S() (respectively A() ) which are obtained as a direct limit of finite symmetric (finit...