1. On groups occurring as absolute centers of finite groups.
- Author
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Fasolă, Georgiana and Tărnăuceanu, Marius
- Subjects
- *
FINITE groups , *AUTOMORPHISM groups , *AUTOMORPHISMS , *CYCLIC groups , *GROUP theory - 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 (H 1) for some subgroup H 1 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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