2023/03/27 by Georgiana Fasolă, Marius Tărnăuceanu, Fasolă, Georgiana +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2303.15636
openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(H1) for some subgroup H1 of H and vice versa. In this paper, we determine completely \rm 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.