Superpositions of free Fox derivations

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Superpositions of free Fox derivations	677 KB	Adobe Acrobat PDF	Read	Download
DOI Доступ к ресурсу на сайте издателя			10.17223/20710410/56/3

Title: Superpositions of free Fox derivations
Title: Суперпозиции свободных производных Фокса
Creator: Romankov, V. A.
Date: 2022
DOI: 10.17223/20710410/56/3
Description: Fox derivations are an effective tool for studying free groups and their group rings. Let Fr be a free group of nite rank r with basis {f1;...; fr}. For every i, the partial Fox derivations ∂/∂fi and ∂/∂f-1i are dened on the group ring Z[Fr]. For k > 2, their superpositions Dfi = ∂/∂fik ○...○ ∂/∂fi∈1; ∈ = (∈1;...;∈k) ∈ {±1}k; are not Fox derivations. In this paper, we study the properties of superpositions Dfi∈. It is shown that the restrictions of such superpositions to the commutant Fr0 are Fox derivations. As an application of the obtained results, it is established that for any rational subset R of Fr0 and any i there are parameters k and ∈ such that R is annihilated by Dfi∈.