Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Garreta, Albert"'
Autor:
Ciobanu, Laura, Garreta, Albert
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more generally, on ext
Externí odkaz:
http://arxiv.org/abs/2204.13946
We study systems of polynomial equations in infinite finitely generated commutative associative rings with an identity element. For each such ring $R$ we obtain an interpretation by systems of equations of a ring of integers $O$ of a finite field ext
Externí odkaz:
http://arxiv.org/abs/2012.09787
We study metabelian groups $G$ given by full rank finite presentations $\langle A \mid R \rangle_{\mathcal{M}}$ in the variety $\mathcal{M}$ of metabelian groups. We prove that $G$ is a product of a free metabelian subgroup of rank $\max\{0, |A|-|R|\
Externí odkaz:
http://arxiv.org/abs/2006.06371
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all non-trivial words
Externí odkaz:
http://arxiv.org/abs/1911.02117
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group. Our results
Externí odkaz:
http://arxiv.org/abs/1910.09000
Autor:
Garreta, Albert, Gray, Robert D.
We investigate systems of equations and the first-order theory of one-relator monoids. We describe a family $\mathcal{F}$ of one-relator monoids of the form $\langle A\mid w=1\rangle$ where for each monoid $M$ in $\mathcal{F}$, the longstanding open
Externí odkaz:
http://arxiv.org/abs/1908.00098
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We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc), which satisfy some natural "non-commutativity" conditio
Externí odkaz:
http://arxiv.org/abs/1805.04085
We study systems of polynomial equations in several classes of finitely generated rings and algebras. For each ring $R$ (or algebra) in one of these classes we obtain an interpretation by systems of equations of a ring of integers $O$ of a finite fie
Externí odkaz:
http://arxiv.org/abs/1805.02573
Let $p$ be a prime and let $G$ be a subgroup of a Sylow pro-$p$ subgroup of the group of automorphisms of the $p$-adic tree. We prove that if $G$ is fractal and $|G':\mathrm{st}_G(1)'|=\infty$, then the set $L(G)$ of left Engel elements of $G$ is tri
Externí odkaz:
http://arxiv.org/abs/1801.04595