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On groups occurring as absolute centers of finite groups.
- 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]
- Subjects :
- *FINITE groups
*AUTOMORPHISM groups
*AUTOMORPHISMS
*CYCLIC groups
*GROUP theory
Subjects
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