| Suppose G is a finite group and H is a subgroup of G. If there exists a subgroup K of G such that G=HK and H∩K=1, then K is called a complement of H in G. This paper determined finite p-groups G whose subgroups not contained in Φ(G) have complements. In addition, we also determined abelian p-groups, metacyclic p-groups and Argroups G whose cyclic (abelian, non-abelian) subgroups not contained in Φ(G) have complements, where t≤3. |
