Results 11 to 20 of about 3,179 (217)
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
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
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
Journal of Algebra, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carter, Roger
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A Tree-Based Model for Addressing Sparsity and Taxa Covariance in Microbiome Compositional Count Data. [PDF]
Stat MedABSTRACT Microbiome compositional data are often high‐dimensional, sparse, and exhibit pervasive cross‐sample heterogeneity. We introduce the “logistic‐tree normal” (LTN) model, a generative model that allows flexible covariance among the microbiome taxa, enables scalable computation, and effectively captures other key characteristics of microbiome ...
Wang Z, Mao J, Ma L.
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The Projective Special Linear Group PSL(4,2). [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2009 :The present study deals with conjugacy classes for the projective linear group. The study of conjugacy classes has a great and important role; in hand it is an introductory step to study the general linear group and also the maximal subgroup in it.We ...
Muthana A. Mahmood, Alaa Adnan Auad
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The transitivity of primary conjugacy in regular ω-semigroups
Open Mathematics, 2022 The conjugacy relation plays an important role in group theory and the conjugacy relation of groups has been generalized to semigroups in various methods by several authors.
Liu Xin, Wang Shoufeng
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Countably recognizable classes of groups with restricted conjugacy classes [PDF]
International Journal of Group Theory, 2018 A group class ${ X}$ is said to be countably recognizable if a group belongs to ${X}$ whenever all its countable subgroups lie in ${X}$. It is proved here that most of the relevant classes of groups defined by restrictions on the conjugacy classes are ...
Francesco de Giovanni, Marco Trombetti
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