W.H. Mills has determined, for a finitely generated abelian group G, the regular subgroups N≅G of S(G), the group of permutations on the set G, which have the same holomorph as G, that is, such that NS(G)(N)=NS(G)(ρ(G)), where ρ is the (right) regular representation. We give an alternative approach to Mills' result, which relies on a characterization of the regular subgroups of NS(G)(ρ(G)) in terms of commutative ring structures on G. We are led to solve, for the case of a finitely generated abelian group G, the following problem: given an abelian group (G,+), what are the commutative ring structures (G,+,⋅) such that all automorphisms of G as a group are also automorphisms of G as a ring?
Caranti, A., & Dalla Volta, F. (2017). The multiple holomorph of a finitely generated abelian group. JOURNAL OF ALGEBRA, 481(1), 327-347.
Citazione: | Caranti, A., & Dalla Volta, F. (2017). The multiple holomorph of a finitely generated abelian group. JOURNAL OF ALGEBRA, 481(1), 327-347. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | No |
Titolo: | The multiple holomorph of a finitely generated abelian group |
Autori: | Caranti, A; Dalla Volta, F |
Autori: | DALLA VOLTA, FRANCESCA (Ultimo) |
Data di pubblicazione: | 2017 |
Lingua: | English |
Rivista: | JOURNAL OF ALGEBRA |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2017.03.006 |
Appare nelle tipologie: | 01 - Articolo su rivista |