| Abstrakt: |
Given a construction f on groups, we say that a group G is f -realisable if there is a group H such that G ≅ f (H) , and completely f -realisable if there is a group H such that G ≅ f (H) and every subgroup of G is isomorphic to f (H 1) for some subgroup H 1 of H and vice versa. In this paper, we determine completely Aut -realisable groups. We also study f -realisable groups for f = Z , F , M , D , Φ , where Z (H) , F (H) , M (H) , D (H) and Φ (H) denote the center, the Fitting subgroup, the Chermak–Delgado subgroup, the derived subgroup and the Frattini subgroup of the group H , respectively. [ABSTRACT FROM AUTHOR] |
