Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u ∈ G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the second author done for simple, adjoint G over the complex numbers. When G is simple and adjoint, the previous work of the second author makes our description com...

Every finite non-abelian group of order n has a non-central element whose centralizer exceeding n1/3. The proof does not rely on the classification simple groups, yet it uses Feit-Thompson theorem.

The paper deals with profinite groups in which centralizers are of finite rank. For a positive integer [Formula: see text] we prove that if is group the centralizer every nontrivial element has rank at most text], then either pro-[Formula: or Further, not virtually group, text].

It has been known for a long time that the structure of a finite simple group is intimately connected with the structure of the centralizers of its involutions. An old result of Brauer and Fowler asserts, in fact, that there are at most a finite number of simple groups in which the centralizer of an involution has a given structure. A more specific, pioneering result of Brauer established that ...

Let (AS , S) be an Artin-Tits and X a subset of S ; denote by AX the subgroup of AS generated by X. When AS is of spherical type, we prove that the normalizer and the commensurator of AX in AS are equal and are the product of AX by the quasi-centralizer of AX in AS . Looking to the associated monoids A + S and A + X , we describe the quasi-centralizer of A+X in A + S thanks to results in Coxete...

This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair groups appearing in definition yields permutation group. In this paper, we determine multi-matrix structures centralizer algebras tensor representations

The main result of this work is an explicit construction of p-local subgroups of the Monster, the largest sporadic simple group. The groups constructed are the normalizers in the Monster of certain subgroups of order 32 , 52 , and 72 and have shapes 32+5+10-(Af11 xGL(2, 3)), 52+2+4-(S3xGL(2, 5)), and 72+1+2 • GL(2, 7). These groups result from a general construction which proceeds in three step...

We answer in the negative a question of Hartley about representations finite groups, by constructing examples simple groups with arbitrarily large whose endomorphism ring consists just scalars. show as consequence that there are automorphisms locally group SL(∞,Fq) trivial centralizer. The smallest our is A6 q=9.

Let [Formula: see text] be a finite-dimensional simple Lie superalgebra of type text], or over text]. the simply connected semisimple algebraic group such that Suppose is nilpotent. We describe centralizer in and its center especially. also determine labeled Dynkin diagram for prove theorems relating dimension diagram.