scholarly journals Intersection of conjugacy classes with Bruhat cells in Chevalley groups: The cases SLn(K),GLn(K)

2007 ◽  
Vol 209 (3) ◽  
pp. 703-723 ◽  
Author(s):  
Erich W. Ellers ◽  
Nikolai Gordeev
Keyword(s):  
Conjugacy Classes ◽  
Chevalley Groups ◽  
Bruhat Cells

scholarly journals Intersection of conjugacy classes with Bruhat cells in Chevalley groups

2004 ◽  
Vol 214 (2) ◽  
pp. 245-261 ◽  
Author(s):  
Erich W. Ellers ◽  
Nikolai Gordeev
Keyword(s):  
Conjugacy Classes ◽  
Chevalley Groups ◽  
Bruhat Cells

scholarly journals Calculating conjugacy classes in Sylow -subgroups of finite Chevalley groups of rank six and seven

2014 ◽  
Vol 17 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Simon M. Goodwin ◽  
Peter Mosch ◽  
Gerhard Röhrle
Keyword(s):  
Computer Program ◽  
Explicit Formula ◽  
Chevalley Group ◽  
Conjugacy Classes ◽  
Chevalley Groups ◽  
Sylow Subgroups ◽  
Finite Chevalley Group ◽  
Integer Coefficients ◽  
The Third

AbstractLet$G(q)$be a finite Chevalley group, where$q$is a power of a good prime$p$, and let$U(q)$be a Sylow$p$-subgroup of$G(q)$. Then a generalized version of a conjecture of Higman asserts that the number$k(U(q))$of conjugacy classes in$U(q)$is given by a polynomial in$q$with integer coefficients. In [S. M. Goodwin and G. Röhrle,J. Algebra321 (2009) 3321–3334], the first and the third authors of the present paper developed an algorithm to calculate the values of$k(U(q))$. By implementing it into a computer program using$\mathsf{GAP}$, they were able to calculate$k(U(q))$for$G$of rank at most five, thereby proving that for these cases$k(U(q))$is given by a polynomial in$q$. In this paper we present some refinements and improvements of the algorithm that allow us to calculate the values of$k(U(q))$for finite Chevalley groups of rank six and seven, except$E_7$. We observe that$k(U(q))$is a polynomial, so that the generalized Higman conjecture holds for these groups. Moreover, if we write$k(U(q))$as a polynomial in$q-1$, then the coefficients are non-negative.Under the assumption that$k(U(q))$is a polynomial in$q-1$, we also give an explicit formula for the coefficients of$k(U(q))$of degrees zero, one and two.

scholarly journals Twisted Conjugacy Classes in Chevalley Groups

2015 ◽  
Vol 53 (6) ◽  
pp. 481-501 ◽  
Author(s):  
T. R. Nasybullov
Keyword(s):  
Conjugacy Classes ◽  
Chevalley Groups ◽  
Twisted Conjugacy

scholarly journals Twisted conjugacy classes in twisted Chevalley groups

2020 ◽  
pp. 2250052
Author(s):  
Sushil Bhunia ◽  
Pinka Dey ◽  
Amit Roy
Keyword(s):  
Characteristic Zero ◽  
Conjugacy Classes ◽  
Transcendence Degree ◽  
Chevalley Groups ◽  
Twisted Conjugacy

Let [Formula: see text] be a group and [Formula: see text] be an automorphism of [Formula: see text]. Two elements [Formula: see text] are said to be [Formula: see text]-twisted conjugate if [Formula: see text] for some [Formula: see text]. We say that a group [Formula: see text] has the [Formula: see text]-property if the number of [Formula: see text]-twisted conjugacy classes is infinite for every automorphism [Formula: see text] of [Formula: see text]. In this paper, we prove that twisted Chevalley groups over a field [Formula: see text] of characteristic zero have the [Formula: see text]-property as well as the [Formula: see text]-property if [Formula: see text] has finite transcendence degree over [Formula: see text] or [Formula: see text] is periodic.

scholarly journals On intersections of conjugacy classes and bruhat cells

2010 ◽  
Vol 15 (2) ◽  
pp. 243-260 ◽  
Author(s):  
Kei Yuen Chan ◽  
Jiang-Hua Lu ◽  
Simon Kai-Ming To
Keyword(s):  
Conjugacy Classes ◽  
Bruhat Cells
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