A. Abdollahi

activity

20022023

most citedGroups all of whose undirected Cayley graphs are integral

21 citations · 87 across the 47 of their papers we have counts for

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40 papers · 1 filter

math.GR2022

Nilpotent probability of compact groups

Alireza Abdollahi, Meisam Soleimani Malekan

Let $k$ be any positive integer and $G$ a compact (Hausdorff) group. Let $\mf{np}_k(G)$ denote the probability that $k + 1$ randomly chosen elements $x_{1}, \dots, x_{k + 1}$ satisfy $[x_1…

math.GR2021

Commuting Probability of Compact Groups

Alireza Abdollahi, Meisam soleimani Malekan

For any (Hausdorff) compact group $G$ with the normalized Haar measure $m_{G}$ , denote by $cp (G)$ the probability ${\mathbf m}_{G\times G}(\{(x,y)\in G\times G \;|\;…

math.GR2021★ 1 cited

Compact groups with a set of positive Haar measure satisfying a nilpotent law

Alireza Abdollahi, Meisam soleimani Malekan

The following question is proposed in [4, Question 1.20]: Let $G$ be a compact group, and suppose that $$\mathcal{N}_k(G) = \{(x1,\dots,x_{k+1}) \in G^{k+1} \;\|; [x_1,\dots, x_{k+…

math.GR2020★ 1 cited

Profinite groups with many elements of bounded order

Alireza Abdollahi, Meisam Soleimani Malekan

Lévai and Pyber proposed the following as a conjecture: Let $G$ be a profinite group such that the set of solutions of the equation $x^{n} = 1$ has positive Haar measure. Then $G$ has…

math.GR2020

Compact groups with many elements of bounded order

Meisam Soleimani Malekan, Alireza Abdollahi, Mahdi Ebrahimi

Lévai and Pyber proposed the following as a conjecture: Let $G$ be a profinite group such that the set of solutions of the equation $x^{n} = 1$ has positive Haar measure. Then $G$ has…

math.GR2020★ 1 cited

On finite totally 2-closed groups

Alireza Abdollahi, Majid Arezoomand, Gareth Tracey

An abstract group $G$ is called totally $2$ -closed if $H = H^{(2), Ω}$ for any set $Ω$ with $G ≅ H \leq Sym (Ω)$ , where $H^{(2), Ω}$ is the largest subgroup of $Sym (Ω)$ who…