The aim of this paper is to investigate the behaviour of prime and semiprime subgroups of groups, and their relation with the existence of abelian normal subgroups. In particular, we study the set Spec(G) of all prime subgroups of a group G endowed with the Zariski topology and, among other examples, we construct an infinite group whose proper normal subgroups are prime and form a descending chain of type ω + 1.
Spectra of Groups / Facchini, A.; de Giovanni, F.; Trombetti, M.. - In: ALGEBRAS AND REPRESENTATION THEORY. - ISSN 1386-923X. - (2023). [10.1007/s10468-022-10138-1]
Spectra of Groups
Facchini A.;de Giovanni F.
;Trombetti M.
2023
Abstract
The aim of this paper is to investigate the behaviour of prime and semiprime subgroups of groups, and their relation with the existence of abelian normal subgroups. In particular, we study the set Spec(G) of all prime subgroups of a group G endowed with the Zariski topology and, among other examples, we construct an infinite group whose proper normal subgroups are prime and form a descending chain of type ω + 1.File in questo prodotto:
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