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On groups with cubic polynomial conditions

dc.contributor.authorGrishkov, A. [UNESP]
dc.contributor.authorNunes, R.
dc.contributor.authorSidki, S.
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.contributor.institutionUniversidade Federal de Goiás (UFG)
dc.contributor.institutionUniversidade de Brasília (UnB)
dc.date.accessioned2022-04-28T19:01:05Z
dc.date.available2022-04-28T19:01:05Z
dc.date.issued2015-09-01
dc.description.abstractLet F<inf>d</inf> be the free group of rank d, freely generated by {y1,. . .,yd}, and let DFd be the group ring over an integral domain D. Given a subset E<inf>d</inf> of F<inf>d</inf> containing the generating set, assign to each s in E<inf>d</inf> a monic polynomial ps(x)=xn+cs,n-1xn-1+. . .+cs,1x+cs,0∈D[x] and define the quotient ringA(d,n,Ed)=DFd〈ps(s)|s∈Ed〉ideal. When ps(s) is cubic for all s, we construct a finite set E<inf>d</inf> such that A(d,n,Ed) has finite rank over an extension of D by inverses of some of the coefficients of the polynomials. When the polynomials are all equal to (x-1)<sup>3</sup> and D=Z[16], we construct a finite subset P<inf>d</inf> of F<inf>d</inf> such that the quotient ring A(d,3,Pd) has finite D-rank and its augmentation ideal is nilpotent. The set P<inf>2</inf> is {y1,y2,y1y2,y1-1y2,y12y2,y1y22,[y1,y2]} and we prove that (x-1)3=0 is satisfied by all elements in the image of F<inf>2</inf> in A(2,3,Pd).en
dc.description.affiliationUniversidade Estadual de Sao Paulo
dc.description.affiliationUniversidade Federal de Goias
dc.description.affiliationDepartamento de Matemática, Universidade de Brasília
dc.description.affiliationUnespUniversidade Estadual de Sao Paulo
dc.format.extent344-364
dc.identifierhttp://dx.doi.org/10.1016/j.jalgebra.2015.04.035
dc.identifier.citationJournal of Algebra, v. 437, p. 344-364.
dc.identifier.doi10.1016/j.jalgebra.2015.04.035
dc.identifier.issn1090-266X
dc.identifier.issn0021-8693
dc.identifier.scopus2-s2.0-84930181305
dc.identifier.urihttp://hdl.handle.net/11449/220370
dc.language.isoeng
dc.relation.ispartofJournal of Algebra
dc.sourceScopus
dc.subjectCubic conditions on groups
dc.subjectNon-commutative Groebner
dc.subjectUnipotent groups
dc.titleOn groups with cubic polynomial conditionsen
dc.typeArtigo

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