some results of α-coset groups

We call g to be an α-coset group, if it contains a proper α-invariant normal subgroup n such that nxα = {xg | g ∈ g}, for some automorphism α of g and any x ∈ gn. clearly, if α is identity automorphism of g, one obtains the notion of con-cos groups, which was first introduced by muktibodh in 2006. in the present article, we discuss some properties of the new notion. also, we introduce the concept of α-camina groups and give its connection with the groups of property p, where p is the class of all finite groups such that their α-centres are the same as α-commutator subgroups of order p.