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pro vyhledávání: '"Malekan, Meisam Soleimani"'
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 $[x_1,x_2,\dots,x_{k+1}]=1$. We study the following problem: If $\mf{np}_k(
Externí odkaz:
http://arxiv.org/abs/2208.04666
For any (Hausdorff) compact group $G$ with the normalized Haar measure ${\mathbf m}_G$, denote by ${\rm cp}(G)$ the probability ${\mathbf m}_{G\times G}(\{(x,y)\in G\times G \;|\; xy=yx\})$ of commuting a randomly chosen pair of elements of $G$. Here
Externí odkaz:
http://arxiv.org/abs/2103.11336
The following question is proposed in [4, Question 1.20]: Let $G$ be a compact group, and suppose that $$\mathcal{N}_k(G) = \{(x1,\dots,x_{k+1}) \in G^{k+1} \;\|; [x_1,\dots, x_{k+1}] = 1\}$$ has positive Haar measure in $G^{k+1}$. Does $G$ have an o
Externí odkaz:
http://arxiv.org/abs/2101.11507
L\'evai 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 an open subgroup $H$ and an element $t$ such that all elements of th
Externí odkaz:
http://arxiv.org/abs/2012.13886
L\'evai 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 an open subgroup $H$ and an element $t$ such that all elements of th
Externí odkaz:
http://arxiv.org/abs/2001.06508
We find a necessary condition for zero divisors in complex group algebras of torsion-free groups.
Externí odkaz:
http://arxiv.org/abs/1905.00951
Autor:
Rejali, Ali, Malekan, Meisam Soleimani
Giving a condition for the the amenability of groups, Rosenblatt and Willis, first introduced the concept of configuration. From the beginning of the theory, the question whether the concept of configuration equivalence coincides with the concept of
Externí odkaz:
http://arxiv.org/abs/1605.00781
Autor:
Rejali, Ali, Malekan, Meisam Soleimani
The concept of configuration was first introduced to give a characterization for the amenability of groups. Then the concept of two-sided configuration was suggested to provide normality to study the group structures more efficiently. It has been int
Externí odkaz:
http://arxiv.org/abs/1512.03021
Autor:
Rejali, Ali, Malekan, Meisam Soleimani
The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we investigate
Externí odkaz:
http://arxiv.org/abs/1510.07209
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