Results 11 to 20 of about 3,182 (219)
From conjugacy classes in the Weyl group to semisimple conjugacy classes [PDF]
Pure and Applied Mathematics Quarterly, 2021 Suppose $G$ is a connected complex semisimple group and $W$ is its Weyl group. The lifting of an element of $W$ to $G$ is semisimple. This induces a well-defined map from the set of elliptic conjugacy classes of $W$ to the set of semisimple conjugacy classes of $G$. In this paper, we give a uniform algorithm to compute this map.
Adams, Jeffrey, He, Xuhua, Nie, Sian
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Symmetric groups and conjugacy classes [PDF]
Journal of Group Theory, 2008 Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial $α,β\in S_n$, we prove that the product $α^{S_n}β^{S_n}$ of the conjugacy classes $α^{S_n}$ and $β^{S_n}$ is never a conjugacy class. Furthermore, if n is not even and $n$ is not a multiple of three, then $α^{S_n}β^{S_n}$ is the union of at least three distinct conjugacy ...
Adan-Bante, Edith, Verrill, Helena
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Conjugacy classes of Renner monoids [PDF]
Journal of Algebra, 2013 A reference ([13]) and Corollary 4.5 are added to show the connection between the result in Theorem 4.4 of the previous version and the results in [13]. A paragraph on page 12 is new to show that Theorem 4.4 can also be deduced from the results in [13].
Li, Zhuo, Li, Zhenheng, Cao, Youʼan
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Conjugacy classes in unitriangular matrices [PDF]
Linear Algebra and its Applications, 2003 Let \(G_n=G_n(q)\) be the group of the upper unitriangular matrices of size \(n\times n\) over \(\text{GF}(q)\), the finite field with \(q=p^t\) elements. Higman has conjectured that, for each \(n\), the number of conjugacy classes of elements of \(G_n\) is a polynomial expression in \(q\).
Vera-López, Antonio, Arregi, J.M.
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On spherical twisted conjugacy classes [PDF]
Transformation Groups, 2012 Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group.
Giovanna Carnovale, CARNOVALE, GIOVANNA
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Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes [PDF]
Advances in Mathematics, 2021 Let $G$ be a reductive group over an algebraically closed field and let $W$ be its Weyl group. In a series of papers, Lusztig introduced a map from the set $[W]$ of conjugacy classes of $W$ to the set $[G_u]$ of unipotent classes of $G$. This map, when restricted to the set of elliptic conjugacy classes $[W_e]$ of $W$, is injective.
Adams, Jeffrey, He, Xuhua, Nie, Sian
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Semisimple conjugacy classes and classes in the Weyl group [PDF]
Journal of Algebra, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carter, Roger
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Commuting conjugacy classes graph of the generalized dihedral and dicyclic groups [PDF]
ریاضی و جامعه, 2023 Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a simple graph with the non-central conjugacy classes of $G$ as its vertex set. Two different non-central conjugacy classes $A$ and $B$ are assumed to be adjacent if and only if there are ...
Mohammadali Salahshour
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Groups with Boundedly Černikov Conjugacy Classes [PDF]
Advances in Group Theory and Applications, 2021 A relevant theorem of B.H. Neumann states that if a group G has boundedly finite conjugacy classes, then its commutator subgroup G' is finite. This result has been generalized in previous work, where it is proved in particular that if the orbits of a ...
M. De Falco +3 more
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Commuting Conjugacy Class Graph of G when G / Z(G)~=D2n [PDF]
Mathematics Interdisciplinary Research, 2020 Suppose G is a finite non-abelian group and Γ(G) is a simple graph with the non-central conjugacy classes of G as its vertex set. Two different noncentral conjugacy classes C and B are assumed to be adjacent in Γ(G) if and only if there are elements a ...
Mohammad Ali Salahshour
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