International Conference on Mathematics and Mathematics Education (ICMME-2017), Harran University, Şanlıurfa, 11-13 May 2017, Şanlıurfa, Turkey, 11 March - 13 December 2017, pp.73-74
We deal with the groups having FC-subgroups and define the class of groups.
We provide two points of view and consider such a group as a subgroup of
for some prime p, the McLain groups, or represent as a finitary
permutation group on an infinite set.
Having certain FC-subgroups in groups may provide some opportunities to
figure out the structure of the groups (see [1,Theorem 1.1(b)] for example). In this
vork we give certain useful results. The following is a slightly generalized form of
[4,Theorem 2.4] (see 4 for the definition of the notion “locally degree preserving").
In this study, we obtained the following results:
Let be a perfect locally finite p-group for some prime p. If there exits
such that is an -group for every then there exists a
locally degree-preserving embedding of an epimorphic image of into
for some prime p.
The above result provides a restriction our attention to McLain goups for some
perfect groups (of course if such groups exist)
Define the class of groups as follows:
The normal closure of every two generated subgroup of the group is an FCgroup.
Let be an infinitely generated locally finite -perfect-p-group for some prime
p with trivial center. If is a -group then has an epimorphic image which can be
represented as a finitary permutation group.
Key Words: FC-subgroups, -perfect-p-group, McLain group, finitary
permutation group, perfect group, -group.
International Conference on Mathematics and Mathematics Education
(ICMME-2017), Harran University, Şanlıurfa, 11-13 May 2017
74
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