Search results for "P-nilpotent group"

showing 2 items of 2 documents

Existence of normal Hall subgroups by means of orders of products

2018

Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup 6. As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.

010101 applied mathematicsPure mathematicsp-nilpotent groupsGeneral Mathematics010102 general mathematicsproduct of elements0101 mathematics01 natural sciencesHall subgroupsMathematicsorder of elements
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Left braces and the quantum Yang-Baxter equation

2019

[EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang¿Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang¿Baxter equation.

BracesYang–Baxter equationGeneral MathematicsMathematics::Rings and Algebras010102 general mathematicsP-nilpotent groupYang-Baxter equationContext (language use)01 natural sciencesBraceAlgebraNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics::Quantum Algebra0103 physical sciences010307 mathematical physics0101 mathematicsMATEMATICA APLICADAQuantumMatemàticaMathematics
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