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2.0

Jun 29, 2018
06/18

by
M. Shahryari

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In the space of marked group, we suppose that a sequence $(G_i, X_i)$ converges to $(G,X)$, where $G$ is finitely presented. We obtain an inequality which connects Dehn functions of $G_i$s and $G$. As a result, we show that if a sequence $(K, X_i)$ converges to a hyperbolic marked group, then $K$ is already hyperbolic.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1601.06982

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4.0

Jun 30, 2018
06/18

by
P. Modabberi; M. Shahryari

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In this article, the properties of being equational noetherian, $q_{\omega}$ and $u_{\omega}$-compactness, and equational Artinian are studied from the perspective of the Zariski topology. The equational conditions on the relative free algebras of arbitrary varieties are also investigated.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1401.4389

2
2.0

Jun 30, 2018
06/18

by
M. Shahryari; A. N. Shevlyakov

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We study equationally Noetherian varieties of groups, rings and monoids. Moreover, we describe equationally Noetherian direct powers for these algebraic structures.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1703.03143

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2.0

Jun 30, 2018
06/18

by
M. Shahryari

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A group $G$ is called logically cyclic, if it contains an element $s$ such that every element of $G$ can be defined by a first order formula with parameter $s$. The aim of this paper is to investigate the structure of such groups.

Topics: Mathematics, Group Theory

Source: http://arxiv.org/abs/1406.7621

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5.0

Jun 28, 2018
06/18

by
M. Shahryari

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In this note, we give a new characterization for an algebra to be $\qo$-compact in terms of {\em super-product operations} on the lattice of congruences of the relative free algebra.

Topics: Mathematics, Logic

Source: http://arxiv.org/abs/1508.00325

5
5.0

Jun 28, 2018
06/18

by
M. Shahryari

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We obtain a necessary and sufficient condition for an algebraic set in a group to have a fully characteristic radical. As a result, we see that if the radical of a system of equation $S$ over a group $G$ is fully characteristic, then there exists a class $\mathfrak{X}$ of subgroups of $G$ such that elements of $S$ are identities of $\mathfrak{X}$.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1508.03128

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3.0

Jun 29, 2018
06/18

by
R. Hobbi; M. Shahryari

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In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1606.04207

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90

Jul 20, 2013
07/13

by
H. Khodabandeh; M. Shahryari

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The main aim of this article is to establish a classification of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraically simpleness), and group theory, GTS (group theoretically simpleness). We obtain the necessary and sufficient conditions for a polyadic group to be UAS or GTS.

Source: http://arxiv.org/abs/1203.2125v1

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43

Sep 23, 2013
09/13

by
M. Shahryari

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A Lie algebra $K$ over a field of characteristic zero $E$ is called a completion of a rational Lie algebra $L$, if it contains $L$ as $\mathbb{Q}$-subalgebra and the $E$-span of $L$ is equal to $K$. The class of all completions of a rational Lie algebra is studied in this article.

Source: http://arxiv.org/abs/1212.2116v1

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12

Jun 27, 2018
06/18

by
P. Modabberi; M. Shahryari

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Equational Artinian algebras were introduced in our previous work: {\em Equational conditions in universal algebraic geometry, to appear in Algebra and Logic, 2015}. In this note, we define the notion of {\em radical topology with respect to an algebra $A$} and using the well-known K\"onig lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is noetherian. This completes the analogy between equational noetherian and equational Artinian algebras.

Topics: Group Theory, Mathematics, Logic

Source: http://arxiv.org/abs/1506.00090

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Jul 20, 2013
07/13

by
M. Shahryari

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We show that for any $n$-ary group $(G,f)$, the group $Aut(G,f)$ can be embedded in $Aut(\mathbb{Z}_{n-1}\ltimes G)$ and so we can obtain a class of interesting automorphisms of cyclic extensions.

Source: http://arxiv.org/abs/1203.2123v1

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12

Jun 28, 2018
06/18

by
H. Khodabandeh; M. Shahryari

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Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group $(G, f)=\mathrm{der}_{\theta, b}(G, \cdot)$ is equational noetherian, if and only if the ordinary group $(G, \cdot)$ is equational noetherian. The structure of coordinate polyadic group of algebraic sets in equational noetherian polyadic groups are also determined.

Topics: Group Theory, Mathematics

Source: http://arxiv.org/abs/1508.07726