ICMME-2017 - International Conference on Mathematics and Mathematics Education, Şanlıurfa, Turkey, 11 - 13 May 2017, vol.1, no.1, pp.122-123
We consider certain groups which have no proper subgroup of finite index
such as minimal non-soluble p-groups and give some descriptions of them.
A group which has no proper subgroup of finite index is called -perfect. Let be a class of
groups. If a group G is not in but every proper subgroup of G is in then G is
called a minimal non -group and denoted usually by . Clearly every perfect p-group for some prime p is -perfect and the structure of many -groups is investigated in perfect p-case.
In the present article we mostly take , the class of all soluble groups, as the class , i.e. we consider certain -groups. It not known yet that if locally finite -p-group which is not finitely generated exist. Such
groups are mainly studied in [5], [4], [2], [3] (in some general form) and
given certain descriptions.
Let G be a group and H be a subgroup of G. If is infinite, 1 and for every proper subgroup K of G, Ç is finite, then
G is called a barely transitive group and H is called a point stabilizer.
Though thr definition of barely transitive groups has permutation groups
origin, we use above abstract definition of these groups (see [7]).
We give certain applications of Khukhro-Makarenko Theorem to -groups. Also we provide a corollary to [8,Satz 6]
which is used effectively in most of the cited
articles and give certain applications of it. Finally we define Weak
Fitting groups and a useful class of groups and
give certain results related to these notions.
Key Words:-group,
-groups, -Perfect groups, barely transitive group.
We consider certain groups which have no proper subgroup of finite index
such as minimal non-soluble p-groups and give some descriptions of them.
A group which has no proper subgroup of finite index is called -perfect. Let be a class of
groups. If a group G is not in but every proper subgroup of G is in then G is
called a minimal non -group and denoted usually by . Clearly every perfect p-group for some prime p is -perfect and the structure of many -groups is investigated in perfect p-case.
In the present article we mostly take , the class of all soluble groups, as the class , i.e. we consider certain -groups. It not known yet that if locally finite -p-group which is not finitely generated exist. Such
groups are mainly studied in [5], [4], [2], [3] (in some general form) and
given certain descriptions.
Let G be a group and H be a subgroup of G. If is infinite, 1 and for every proper subgroup K of G, Ç is finite, then
G is called a barely transitive group and H is called a point stabilizer.
Though thr definition of barely transitive groups has permutation groups
origin, we use above abstract definition of these groups (see [7]).
We give certain applications of Khukhro-Makarenko Theorem to -groups. Also we provide a corollary to [8,Satz 6]
which is used effectively in most of the cited
articles and give certain applications of it. Finally we define Weak
Fitting groups and a useful class of groups and
give certain results related to these notions.
Key Words:-group,
-groups, -Perfect groups, barely transitive group.