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On groups occurring as absolute centers of finite groups.

Authors :
Fasolă, Georgiana
Tărnăuceanu, Marius
Source :
Communications in Algebra. 2024, Vol. 52 Issue 5, p1826-1831. 6p.
Publication Year :
2024

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]

Details

Language :
English
ISSN :
00927872
Volume :
52
Issue :
5
Database :
Academic Search Index
Journal :
Communications in Algebra
Publication Type :
Academic Journal
Accession number :
175980239
Full Text :
https://doi.org/10.1080/00927872.2023.2274954