The Krull-Schmidt Theorem Holds for Finite Direct Products of Biuniform Groups

Facchini, Alberto; Lucchini, Andrea

doi:10.1007/s10468-017-9715-y

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G-groups1

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2022

2023

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Cited by 4 publications

(1 citation statement)

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“…Another immediate application of our theory is to G-groups, which we studied in [1,4,5,15,16]. The notion of G-group H is classical.…”

Section: G-groupsmentioning

confidence: 99%

Algebraic structures from the point of view of complete multiplicative lattices

Facchini¹

2022

Preprint

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General results on multiplicative lattices found recently by Facchini, Finocchiaro and Janelidze have been studied in the particular case of groups by Facchini, de Giovanni and Trombetti. In this paper we prove that these results hold not only for the multiplicative lattices of all normal subgroups of a group, but also for much more general multiplicative lattices. Therefore they can be applied to other algebraic structures, for instance to braces.

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“…Another immediate application of our theory is to G-groups, which we studied in [1,4,5,15,16]. The notion of G-group H is classical.…”

Section: G-groupsmentioning

confidence: 99%

Algebraic structures from the point of view of complete multiplicative lattices

Facchini¹

2022

Preprint

Self Cite

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Spectra of Groups

Facchini

Giovanni

Trombetti

2022

Algebr Represent Theor

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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.

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Category ofG-Groups and its Spectral Category

Paniagua

Facchini

2016

Communications in Algebra

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The Krull-Schmidt Theorem Holds for Finite Direct Products of Biuniform Groups

Cited by 4 publications

References 24 publications

Algebraic structures from the point of view of complete multiplicative lattices

Algebraic structures from the point of view of complete multiplicative lattices

Spectra of Groups

Category ofG-Groups and its Spectral Category

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