On groups occurring as absolute centers of finite groups

2023/10/18 by Georgiana Fasolă, Marius Tărnăuceanu, Fasolă, Georgiana +1 · 2 citations
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2310.12372

openalex publication_date 2023/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Denote by L(G) the absolute center of a group G, that is the set of elements of G fixed by all automorphisms of G. By using the structure of the automorphism group of a ZM-group, in this paper we prove that cyclic groups C_N, N∈ℕ^*, are completely L-realisable.

Cited by

• The Reidemeister spectrum of ZM-groups
• Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups

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