On Characterization of Various Finite Subgroups of Abelian Groups

Abstract

The present paper, we characterize finite subgroups. Throughout G always denote a finite group. Let H be a subgroup group of G. We have H ≥ H ∩ H x  1, for any x ϵ G. We call H to be a TI-subgroup of G if H ∩ Hx = H or 1 for any x ϵ G. We have shown that if H is normal in G or if H is of a prime order, then H is a TI-subgroup.