The tits group as a standard subgroup

1982 ◽  
Vol 181 (2) ◽  
pp. 229-252 ◽  
Author(s):  
Michael Aschbacher
Keyword(s):  
Tits Group

scholarly journals On the minimal positive standardizer of a parabolic subgroup of an Artin–Tits group

2018 ◽  
Vol 49 (3) ◽  
pp. 337-359 ◽  
Author(s):  
María Cumplido
Keyword(s):  
Parabolic Subgroup ◽  
Tits Group

Another Existence and Uniqueness Proof of the Tits Group

2008 ◽  
Vol 15 (02) ◽  
pp. 241-278
Author(s):  
Gerhard O. Michler ◽  
Lizhong Wang
Keyword(s):  
Finite Groups ◽  
Existence And Uniqueness ◽  
Frobenius Group ◽  
Nilpotency Class ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Uniqueness Proof ◽  
Groups Of Lie Type ◽  
Uniqueness Criteria ◽  
Tits Group

In this article we give a self-contained existence and uniqueness proof for the Tits simple group T. Parrott gave the first uniqueness proof. Whereas Tits' and Parrott's results employ the theory of finite groups of Lie type, our existence and uniqueness proof follows from the general algorithms and uniqueness criteria for abstract finite simple groups described in the first author's book [11]. All we need from the previous papers is the fact that the centralizer H of the Tits group T is an extension of a 2-group J with order 29 and nilpotency class 3 by a Frobenius group F of order 20 such that the center Z(H) has order 2 and any Sylow 5-subgroup Q of H has a centralizer CJ(Q) ≤ Z(H).

scholarly journals Torsion units for a Ree group, Tits group and a Steinberg triality group

2015 ◽  
Vol 65 (1) ◽  
pp. 139-157
Author(s):  
Joe Gildea
Keyword(s):  
Ree Group ◽  
Torsion Units ◽  
Tits Group

THE BRAID ROOK MONOID

2008 ◽  
Vol 18 (04) ◽  
pp. 779-802 ◽  
Author(s):  
EDDY GODELLE
Keyword(s):  
Group Theory ◽  
Coxeter Group ◽  
Coxeter Groups ◽  
Hecke Algebra ◽  
Linear Algebraic Group ◽  
Weyl Groups ◽  
Rook Monoid ◽  
Algebraic Monoid ◽  
Tits Group

In linear algebraic monoid theory, the Renner monoids play the role of the Weyl groups in linear algebraic group theory. It is well known that Weyl groups are Coxeter groups, and that we can associate a Hecke algebra and an Artin–Tits group to each Coxeter group. The question of the existence of a Hecke algebra associated with each Renner monoid has been positively answered. In this paper we discuss the question of the existence of an equivalent of the Artin–Tits groups in the framework of Renner monoids. We consider the seminal case of the rook monoid and introduce a new length function.

scholarly journals Some designs and codes invariant under the Tits group

2017 ◽  
Vol 11 (1) ◽  
pp. 77-82 ◽  
Author(s):  
Jamshid Moori ◽  
◽  
Amin Saeidi
Keyword(s):  
Tits Group

scholarly journals ACYLINDRICAL HYPERBOLICITY OF ARTIN–TITS GROUPS ASSOCIATED WITH TRIANGLE-FREE GRAPHS AND CONES OVER SQUARE-FREE BIPARTITE GRAPHS

2020 ◽  
pp. 1-14
Author(s):  
MOTOKO KATO ◽  
SHIN-ICHI OGUNI
Keyword(s):  
Bipartite Graphs ◽  
Large Type ◽  
Central Quotient ◽  
Tits Group

Abstract It is conjectured that the central quotient of any irreducible Artin–Tits group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin–Tits groups that are known to be CAT(0) groups by a result of Brady and McCammond, that is, Artin–Tits groups associated with graphs having no 3-cycles and Artin–Tits groups of almost large type associated with graphs admitting appropriate directions. In particular, the latter family contains Artin–Tits groups of large type associated with cones over square-free bipartite graphs.

ORDERINGS ON ARTIN–TITS GROUPS

2008 ◽  
Vol 18 (06) ◽  
pp. 1035-1066
Author(s):  
HERVE SIBERT
Keyword(s):  
Partial Order ◽  
Partial Ordering ◽  
Necessary Condition ◽  
Coxeter Graph ◽  
Type D ◽  
Tits Group

We prove that a construction similar to that described by Dehornoy in the case of braids is possible for every Artin–Tits group, yielding a partial ordering. A necessary condition for this partial order to be linear is that the associated Coxeter graph consists only of disjoint lines. So, in particular, type D is dismissed.

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