scholarly journals Bar operators for quasiparabolic conjugacy classes in a Coxeter group

2016 ◽  
Vol 453 ◽  
pp. 325-363 ◽  
Author(s):  
Eric Marberg
Keyword(s):  
Coxeter Group ◽  
Conjugacy Classes

scholarly journals Conjugacy classes of involutions in Coxeter groups

1982 ◽  
Vol 26 (1) ◽  
pp. 1-15 ◽  
Author(s):  
R.W. Richardson
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Equivalence Classes ◽  
Conjugacy Classes ◽  
Elementary Method

In this paper we give an elementary method for classifying conjugacy classes of involutions in a Coxeter group (W, S). The classification is in terms of (W-equivalence classes of certain subsets of S).

scholarly journals Special involutions and bulky parabolic subgroups in finite Coxeter groups

2005 ◽  
Vol 79 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Götz Pfeiffer ◽  
Gerhard Röhrle
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Hyperplane Arrangement ◽  
Conjugacy Classes ◽  
Parabolic Subgroups ◽  
Finite Coxeter Group

AbstractThe conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.

scholarly journals Conjugacy classes and automorphisms of twin groups

2020 ◽  
Vol 32 (5) ◽  
pp. 1095-1108
Author(s):  
Tushar Kanta Naik ◽  
Neha Nanda ◽  
Mahender Singh
Keyword(s):  
Symmetric Group ◽  
Coxeter Group ◽  
Fibonacci Sequence ◽  
Recursive Formula ◽  
Conjugacy Classes ◽  
Structural Aspects

AbstractThe twin group {T_{n}} is a right-angled Coxeter group generated by {n-1} involutions, and the pure twin group {\mathrm{PT}_{n}} is the kernel of the natural surjection from {T_{n}} onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of conjugacy classes of involutions in {T_{n}}, which, quite interestingly, is related to the well-known Fibonacci sequence. We also derive a recursive formula for the number of z-classes of involutions in {T_{n}}. We give a new proof of the structure of {\operatorname{Aut}(T_{n})} for {n\geq 3}, and show that {T_{n}} is isomorphic to a subgroup of {\operatorname{Aut}(\mathrm{PT}_{n})} for {n\geq 4}. Finally, we construct a representation of {T_{n}} to {\operatorname{Aut}(F_{n})} for {n\geq 2}.

Tits Indices

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Coxeter Group ◽  
Coxeter System ◽  
Relative Rank ◽  
Coxeter Diagram ◽  
The Absolute ◽  
Relative Type

This chapter introduces the notion of a Tits index and the notion of the relative Coxeter diagram of a Tits index. It first defines a Tits index, which can be anisotropic or isotropic, quasi-split or split, before considering a number of propositions regarding compatible representations. It then gives a proof of the theorem that includes two assumptions about a Coxeter system, focusing on the absolute Coxeter system, the relative Coxeter system, and the relative Coxeter group of the Tits index, as well as the absolute Coxeter diagram (or absolute type), the relative Coxeter diagram (or relative type), and the absolute rank and the relative rank of the Tits index. The chapter concludes with some observations about the case that (W, S) is spherical, irreducible or affine.

scholarly journals Groups with boundedly finite conjugacy classes of commutators

2018 ◽  
Vol 69 (3) ◽  
pp. 1047-1051 ◽  
Author(s):  
Gláucia Dierings ◽  
Pavel Shumyatsky
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

scholarly journals A classification of spherical conjugacy classes

2016 ◽  
Vol 285 (1) ◽  
pp. 63-91
Author(s):  
Mauro Costantini
Keyword(s):  
Conjugacy Classes

A NOTE ON THE NUMBER OF ZEROS IN THE COLUMNS OF THE CHARACTER TABLE OF A GROUP

2012 ◽  
Vol 12 (02) ◽  
pp. 1250150 ◽  
Author(s):  
JINSHAN ZHANG ◽  
ZHENCAI SHEN ◽  
SHULIN WU
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Conjugacy Classes ◽  
Character Table ◽  
Number Of Zeros

The finite groups in which every irreducible character vanishes on at most three conjugacy classes were characterized [J. Group Theory13 (2010) 799–819]. Dually, we investigate the finite groups whose columns contain a small number of zeros in the character table.

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