Groups with only normal and abnormal subgroups

AbstractThe concept of an abnormal subgroup of a group G is, in a sense, opposite of that of a normal subgroup of G. Precisely speaking, the only subgroup of G that is both normal and abnormal in G is G itself. A maximal subgroup of a group G is either normal or abnormal. Here, we study those finite groups in which each subgroup is either normal or abnormal. Theorem 3 characterizes all such groups