Some Finite Groups With All Subgroups Of Order2Being Conjugate-Permutable Subgroups

Subgroups influence the structures of groups, normal subgroups of a group play an important role in group theory. In the development of group theory, some sub-groups such as subnormal subgroup, quasinormal subgroup, conjugate-permutable subgroup, and so on, which condition is weaker than the one of normal subgroups in a group are put forward. A Subgroup H of a group G is called conjugate-permutable, if H9H=HH9, for all.gEG.written H <c-p G.It is an effective way to study the structure of a finite group by using the conjugate-permutable subgroups on which a lot of famous theorems were set up. In this paper, the author utilize properties of conjugate-permutable special subgroups, classifing groups of order4p,4p2,4pq and8p in which all subgroups of order2are conjugate-permutable subgroupsThe paper consists of the following three sections:In section one:we introduce the research background of conjugate-permutable subgroups.In section two: we introduce some basic concepts and lemma as used in this paper.In section three:we classify the groups of order4p,4p2.4pq and8p in which all subgroups of order2are conjugate-permutable subgroups...