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Pooya Vahidi Ferdowsi - One of the best experts on this subject based on the ideXlab platform.
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strong amenability and the infinite Conjugacy Class property
Inventiones Mathematicae, 2019Co-Authors: Joshua Frisch, Omer Tamuz, Pooya Vahidi FerdowsiAbstract:A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite Conjugacy Class property.
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choquet deny groups and the infinite Conjugacy Class property
Annals of Mathematics, 2019Co-Authors: Joshua Frisch, Omer Tamuz, Yair Hartman, Pooya Vahidi FerdowsiAbstract:A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure μ on G, it holds that all bounded μ-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite Conjugacy Class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.
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non virtually nilpotent groups have infinite Conjugacy Class quotients
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Pooya Vahidi FerdowsiAbstract:We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite Conjugacy Class (ICC) propoerty. This proof is a modern presentation of the original proof, by McLain (1956) and Duguid and McLain (1956).
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choquet deny groups and the infinite Conjugacy Class property
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Omer Tamuz, Yair Hartman, Pooya Vahidi FerdowsiAbstract:A countable discrete group $G$ is said to be Choquet-Deny if it has a trivial Poisson boundary for every generating probability measure. We show that a finitely generated group $G$ is Choquet-Deny if and only if it is virtually nilpotent. Moreover, when $G$ is not virtually nilpotent, then the Poisson boundary is non-trivial for a generating measure that is symmetric and has finite entropy. For general countable discrete groups, we show that $G$ is Choquet-Deny if and only if none of its quotients have the infinite Conjugacy Class property.
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strong amenability and the infinite Conjugacy Class property
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Omer Tamuz, Pooya Vahidi FerdowsiAbstract:A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a countable discrete group is strongly amenable if and only if none of its quotients have the infinite Conjugacy Class property.
Xiuyun Guo - One of the best experts on this subject based on the ideXlab platform.
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on the Conjugacy Class lengths of finite groups
Siberian Mathematical Journal, 2010Co-Authors: Qingjun Kong, Xiuyun GuoAbstract:We investigate how certain arithmetical conditions on the Conjugacy Class lengths of all elements of prime power or biprimary orders of G influence the p-structure of G. In particular, the structure of p-complements of G is described. Some results in [1] and [2] are generalized.
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on Conjugacy Class sizes of the p elements with prime power order
Algebra Colloquium, 2009Co-Authors: Xianhe Zhao, Xiuyun GuoAbstract:In this paper we prove that a finite p-solvable group G is solvable if its every Conjugacy Class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every Conjugacy Class size of 2′-elements with prime power order.
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on the normal subgroup with exactly two g Conjugacy Class sizes
Chinese Annals of Mathematics Series B, 2009Co-Authors: Xianhe Zhao, Xiuyun GuoAbstract:Let G be a finite group with a non-central Sylow r-subgroup R, Z(G) the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-Conjugacy Class size of every element of N is either 1 or m. Particularly, it is shown that N is Abelian if N ∩ Z(G) = 1 and the G-Conjugacy Class size of every element of N is either 1 or m.
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On Conjugacy Class Sizes of the p′-Elements with Prime Power Order
Algebra Colloquium, 2009Co-Authors: Xianhe Zhao, Xiuyun GuoAbstract:In this paper we prove that a finite p-solvable group G is solvable if its every Conjugacy Class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every Conjugacy Class size of 2′-elements with prime power order.
Andrey Mudrov - One of the best experts on this subject based on the ideXlab platform.
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quantum sphere mathbb s 4 as a non levi Conjugacy Class
Letters in Mathematical Physics, 2012Co-Authors: Andrey MudrovAbstract:We construct a \({U_\hbar(\mathfrak{sp}(4))}\)-equivariant quantization of the four-dimensional complex sphere \({\mathbb{S}^4}\) regarded as a Conjugacy Class, Sp(4)/Sp(2) × Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum polynomial algebra \({\mathbb{C}_\hbar[\mathbb{S}^4]}\) on a highest weight module of \({U_\hbar(\mathfrak{sp}(4))}\).
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quantum sphere s 4 as a non levi Conjugacy Class
arXiv: Quantum Algebra, 2011Co-Authors: Andrey MudrovAbstract:We construct a U_h(sp(4))-equivariant quantization of the four-dimensional complex sphere S^4 regarded as a Conjugacy Class, Sp(4)/Sp(2)x Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum polynomial algebra C_h[S^4] on a highest weight module of U_h(sp(4)).
Joshua Frisch - One of the best experts on this subject based on the ideXlab platform.
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strong amenability and the infinite Conjugacy Class property
Inventiones Mathematicae, 2019Co-Authors: Joshua Frisch, Omer Tamuz, Pooya Vahidi FerdowsiAbstract:A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite Conjugacy Class property.
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choquet deny groups and the infinite Conjugacy Class property
Annals of Mathematics, 2019Co-Authors: Joshua Frisch, Omer Tamuz, Yair Hartman, Pooya Vahidi FerdowsiAbstract:A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure μ on G, it holds that all bounded μ-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite Conjugacy Class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.
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non virtually nilpotent groups have infinite Conjugacy Class quotients
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Pooya Vahidi FerdowsiAbstract:We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite Conjugacy Class (ICC) propoerty. This proof is a modern presentation of the original proof, by McLain (1956) and Duguid and McLain (1956).
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choquet deny groups and the infinite Conjugacy Class property
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Omer Tamuz, Yair Hartman, Pooya Vahidi FerdowsiAbstract:A countable discrete group $G$ is said to be Choquet-Deny if it has a trivial Poisson boundary for every generating probability measure. We show that a finitely generated group $G$ is Choquet-Deny if and only if it is virtually nilpotent. Moreover, when $G$ is not virtually nilpotent, then the Poisson boundary is non-trivial for a generating measure that is symmetric and has finite entropy. For general countable discrete groups, we show that $G$ is Choquet-Deny if and only if none of its quotients have the infinite Conjugacy Class property.
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strong amenability and the infinite Conjugacy Class property
arXiv: Group Theory, 2018Co-Authors: Joshua Frisch, Omer Tamuz, Pooya Vahidi FerdowsiAbstract:A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a countable discrete group is strongly amenable if and only if none of its quotients have the infinite Conjugacy Class property.
Guiyun Chen - One of the best experts on this subject based on the ideXlab platform.
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recognizing simple k_4 groups by few special Conjugacy Class sizes
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Yanheng Chen, Guiyun ChenAbstract:In 1987, J. G. Thompson put forward the following conjecture: Let G be a finite group with trivial center. If L is a finite simple group satisfying that\(N(G)=N(L)\), then\(G\cong L\). The second author proved above conjecture holds for finite simple groups with non-connected prime graphs. Vasilev proved above conjecture holds for two simple groups with connected prime graphs: \(A_{10}\) and \(L_4(4)\). N. Ahanjideh proved that Thompson’s conjecture is true for \(L_n(q)\). The authors are interested in if it is possible to weaken the conditions in the conjecture. A finite simple group is called a simple \(K_n-\)group if its order is divisible by exactly \(n\) distinct primes. Here, the authors prove that simple \(K_4-\)groups are characterized by their orders and few special Conjugacy Class sizes, which implies that Thompson’s conjecture is valid for simple \(K_4-\)groups.
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on coprime g Conjugacy Class sizes in a normal subgroup
Acta Mathematica Sinica, 2014Co-Authors: Xianhe Zhao, Guiyun ChenAbstract:Let N be a normal subgroup of a group G. Suppose that the positive integers m > n are two longest non-central G-Conjugacy Class sizes of N with (m, n) = 1. The purpose of this paper is to determine the structure of N and give the N-Conjugacy Class sizes of the elements in N under that assumption that m is square free.
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a lower bound of Conjugacy Class length of symmetric group
Journal of Discrete Mathematical Sciences and Cryptography, 2014Co-Authors: Yanheng Chen, Guiyun ChenAbstract:AbstractIn this paper, an inequality is proved and using this inequality, we obtain a lower bound of all Conjugacy Class lengths of Sn, where Sn is a symmetric group of degree n, n ≥ 3. Further using another inequality, we get a lower bound (only depend on n) of some Conjugacy Class lengths of symmetric group Sn, n ≥ 15.
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recognizing l 2 p by its order and one special Conjugacy Class size
Journal of Inequalities and Applications, 2012Co-Authors: Yanheng Chen, Guiyun ChenAbstract:In the past thirty years, many authors investigated some quantitative characterizations of finite groups, especially finite simple groups, such as quantitative characterizations by group order and element orders, by the set of lengths of Conjugacy Classes, by dimensions of irreducible characters, etc. In this article the projective special linear group L2(p) is characterized by its order and one special Conjugacy Class size, where p is a prime. This work implies that Thompson’s conjecture holds for L2(p). MSC: 20D08; 20D60