scholarly journals Limit formulas for groups with one conjugacy class of Cartan subgroups

2008 ◽  
Vol 58 (4) ◽  
pp. 1213-1232
Author(s):  
Mladen Božičević
Keyword(s):  
Conjugacy Class ◽  
Cartan Subgroups

scholarly journals CONJUGACY OF CARTER SUBGROUPS IN GROUPS OF FINITE MORLEY RANK

2008 ◽  
Vol 08 (01) ◽  
pp. 41-92 ◽  
Author(s):  
OLIVIER FRÉCON
Keyword(s):  
Conjugacy Class ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Morley Rank ◽  
Minimal Counterexample ◽  
Finite Morley Rank ◽  
Cartan Subgroups

The Cherlin–Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are analogous to Cartan subgroups in algebraic groups.

scholarly journals The structure of Cartan subgroups in Lie groups

2021 ◽  
Author(s):  
Arunava Mandal ◽  
Riddhi Shah
Keyword(s):  
Lie Groups ◽  
Cartan Subgroups

scholarly journals A NONDEGENERATE EXCHANGE MOVE ALWAYS PRODUCES INFINITELY MANY NONCONJUGATE BRAIDS

2019 ◽  
pp. 1-4
Author(s):  
TETSUYA ITO
Keyword(s):  
Conjugacy Class

We show that if a link $L$ has a closed $n$ -braid representative admitting a nondegenerate exchange move, an exchange move that does not obviously preserve the conjugacy class, $L$ has infinitely many nonconjugate closed $n$ -braid representatives.

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 $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

scholarly journals Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem

2010 ◽  
Vol 130 (12) ◽  
pp. 2753-2772 ◽  
Author(s):  
Burcu Baran
Keyword(s):  
Class Number ◽  
Modular Curves ◽  
Cartan Subgroups

Prime Divisors ofp-regular Conjugacy Class Sizes

2015 ◽  
Vol 43 (8) ◽  
pp. 3365-3371 ◽  
Author(s):  
Yang Liu ◽  
Ziqun Lu
Keyword(s):  
Conjugacy Class ◽  
Conjugacy Class Sizes ◽  
Prime Divisors

Algebraic groups with a distinguished conjugacy class

1995 ◽  
Vol 7 (7) ◽  
Author(s):  
Maria Rosaria Enea
Keyword(s):  
Conjugacy Class ◽  
Algebraic Groups
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