M. Sohrabi

activity

20092026

most citedElementary coordinatization of finitely generated nilpotent groups

6 citations · 16 across the 11 of their papers we have counts for

collaborators

12 papers

math.LO2026

Arbitrary models of the complete first-order theories of FDZ-rings

Mahmood Sohrabi

In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by t…

math.GR2024

Groups elementarily equivalent to the classical matrix groups

Alexei G. Myasnikov, Mahmood Sohrabi

In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as $G L_{n} (F), S L_{n} (F)$ and $T_{n} (F)$ over a field $F$ provided…

math.LO2021

Rich groups, weak second order logic, and applications

Olga Kharlampovich, Alexei Myasnikov, Mahmood Sohrabi

In this paper we initiate a study of first-order rich groups, i.e., groups where the first-order logic has the same power as the weak second order logic. Surprisingly, there are qu…

math.GR2020★ 5 cited

Bi-interpretability with $Z$ and models of the complete elementary theories of $SL_{n} (O)$ , $T_{n} (O)$ and $GL_{n} (O)$ , $n \geq 3$

Mahmood Sohrabi, Alexei G. Myasnikov

Let $O$ be the ring of integers of a number field, and let $n \geq 3$ . This paper studies bi-interpretability of the ring of integers $Z$ with the special linear…

math.RA2016

On elementary equivalence of rings with a finitely generated additive group

Alexei Miasnikov, Mahmood Sohrabi

In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings…

math.GR2016★ 1 cited

On groups elementarily equivalent to a group of triangular matrices $T_{n} (R)$

Alexei Miasnikov, Mahmood Sohrabi

In this paper we investigate the structure of groups elementarily equivalent to the group $T_{n} (R)$ of all invertible upper triangular $n \times n$ matrices, where $n \geq 3$ and $R$ …

math.GR2015

Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group

Funda Gul, Alexei G. Myasnikov, Mahmood Sohrabi

In this paper we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups $G$ into unitriangular groups $U T_{n} (Z)$ . We also pro…

math.GR2015★ 4 cited

Magnus embedding and algorithmic properties of groups $F / N^{(d)}$

Funda Gul, Mahmood Sohrabi, Alexander Ushakov

In this paper we further study properties of Magnus embedding, give a precise reducibility diagram for Dehn problems in groups of the form $F / N^{(d)}$ , and provide a detailed answe…

math.GR2014

$ω$ -stability and Morley rank of bilinear maps, rings and nilpotent groups

Alexei G. Myasnikov, Mahmood Sohrabi

In this paper we study the algebraic structure of $ω$ -stable bilinear maps, arbitrary rings and nilpotent groups. We will also provide rather complete structure theorems for the ab…

math.GR2013★ 6 cited

Elementary coordinatization of finitely generated nilpotent groups

A. G. Myasnikov, Mahmood Sohrabi

This paper has two main parts. In the first part we develop an elementary coordinatization for any nilpotent group $G$ taking exponents in a binomial principal ideal domain (PID) $…

math.GR2010

Groups elementarily equivalent to a free nilpotent group of finite rank

Alexei G. Myasnikov, Mahmood Sohrabi

In this paper we give a complete algebraic description of groups elementarily equivalent to a given free nilpotent group of finite rank.

math.GR2009

Groups Elementarily Equivalent to a Free 2-nilpotent Group of Finite Rank

Alexei G. Myasnikov, Mahmood Sohrabi

In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.

Arbitrary models of the complete first-order theories of FDZ-rings

Groups elementarily equivalent to the classical matrix groups

Rich groups, weak second order logic, and applications

Bi-interpretability with Z and models of the complete elementary theories of SLn​(O), Tn​(O) and GLn​(O), n≥3

On elementary equivalence of rings with a finitely generated additive group

On groups elementarily equivalent to a group of triangular matrices Tn​(R)

Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group

Magnus embedding and algorithmic properties of groups F/N(d)

ω-stability and Morley rank of bilinear maps, rings and nilpotent groups

Elementary coordinatization of finitely generated nilpotent groups

Groups elementarily equivalent to a free nilpotent group of finite rank

Groups Elementarily Equivalent to a Free 2-nilpotent Group of Finite Rank

Bi-interpretability with $Z$ and models of the complete elementary theories of $SL_{n} (O)$ , $T_{n} (O)$ and $GL_{n} (O)$ , $n \geq 3$

On groups elementarily equivalent to a group of triangular matrices $T_{n} (R)$

Magnus embedding and algorithmic properties of groups $F / N^{(d)}$

$ω$ -stability and Morley rank of bilinear maps, rings and nilpotent groups