Configuration of Groups Containing Generalized Normal Subgroups

This paper aims to identify unique symmetric presentation of normal subgroups. It is often observed that a subgroup X of a group G is considered almost normal if the index |G:NG(X)| is finite, while X is termed nearly normal if it possesses a finite index in its normal closure . We introduce some concepts related to commutators and abelian subgroups. This paper explores the structure of groups in which every infinite subgroup is either almost normal or nearly normal.