The Experts below are selected from a list of 1902 Experts worldwide ranked by ideXlab platform
A. Ivanov - One of the best experts on this subject based on the ideXlab platform.
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Generating sets consisting of pairwise Conjugate Elements
International Journal of Algebra and Computation, 2017Co-Authors: A. IvanovAbstract:We consider groups [Formula: see text] which have generating sets consisting of pairwise Conjugate Elements. We introduce a natural condition on such sets, namely path-connectedness, which has strong consequences when [Formula: see text] acts on a real tree. The main result of the paper states that the group of type-preserving automorphisms of a regular simplicial tree has a generating set with this property.
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Generating sets consisting of pairwise Conjugate Elements
International Journal of Algebra and Computation, 2017Co-Authors: A. IvanovAbstract:We consider groups G which have generating sets consisting of pairwise Conjugate Elements. We introduce a natural condition on such sets, namely path-connectedness, which has strong consequences when G acts on a real tree. The main result of the paper states that the group of type-preserving automorphisms of a regular simplicial tree has a generating set with this property.
S. A. Zyubin - One of the best experts on this subject based on the ideXlab platform.
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Conjugately dense subgroups of free products of groups with amalgamation
Algebra and Logic, 2006Co-Authors: S. A. ZyubinAbstract:A subgroup having non-empty intersection with each class of Conjugate Elements of the group is said to be Conjugately dense. It is shown that, under certain conditions, the number of Conjugately dense subgroups in a free product with amalgamation is not less than some cardinal. As a consequence, P. Neumann’s conjecture in the Kourovka notebook (Question 6.38) is refuted. It is also stated that a modular group and a non-Abelian group of countable or finite rank possess continuum many pairwise non-Conjugate Conjugately dense subgroups.
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Conjugately Dense Subgroups of Locally Finite Chevalley Groups of Lie Rank 1
Siberian Mathematical Journal, 2003Co-Authors: S. A. Zyubin, V. M. LevchukAbstract:Of interest are the subgroups of various groups which have nonempty intersection with each class of Conjugate Elements of the group under study. We call these subgroups Conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all Conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.
Jiping Zhang - One of the best experts on this subject based on the ideXlab platform.
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Finite Groups With Many Conjugate Elements
Journal of Algebra, 1994Co-Authors: Jiping ZhangAbstract:Abstract In this paper we prove the following long-standing conjecture in the theory of finite groups: Finite solvable groups with no two distinct conjugacy classes of the same length are isomorphic to the symmetric group of degree 3.
Wei Zhou - One of the best experts on this subject based on the ideXlab platform.
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finite p groups with small subgroups generated by two Conjugate Elements
Archiv der Mathematik, 2013Co-Authors: Wei ZhouAbstract:In this paper, we study the properties of a finite p-group G such that \({|\langle x, x^y \rangle:\langle x \rangle| \leq p}\) for all \({x,y \in G}\). Such groups relate to a problem posed by Berkovich and Janko (Groups of prime order, Walter de Gruyter, Berlin, vol. 3, 2011) (Problem 1762). For such a group G, we mainly get the exponent of G′ and the nilpotent class of G.
Jamal Teymouri - One of the best experts on this subject based on the ideXlab platform.
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On Conjugate Elements in a semigroup and semigroup diagrams
Semigroup Forum, 2016Co-Authors: Paul A. Cummings, Jamal TeymouriAbstract:Semigroup derivation diagrams provide a geometric model for when a pair of positive words represent the same element of a semigroup S given by a semigroup presentation \(P=\langle X \, \vert \, R\rangle \). They are analogous to Lyndon-van Kampen group diagrams that model words representing the identity element in a group G. One key property of semigroup derivation diagrams is that they contain no internal vertices of either in-degree zero or out-degree zero. In this note we introduce classes of annular semigroup diagrams which also have, or nearly have, this key property. For our principal results, we use these (restricted) classes of annular semigroup diagrams to model some versions of conjugacy in semigroups. This is, intentionally, a semigroup analogue of the annular group diagrams first used by Paul Schupp to model conjugacy over presentations for a group.