(Received) Let G, H and E be subgroups of a nite nilpotent permutation group of degree n. We describe the theory and implementation of an algorithm to compute the normalizer N G (H) in time polynomial in n, and we give a modiied algorithm to determine whether H and E are conjugate under G and, if so, to nd a conjugating element of G. Other algorithms produce the intersection G \ H and the centr...

Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred homomorphism to the normalizer of the maximal torus; i.e. that “norm...

Let G be a connected reductive group over an algebraically closed field $\Bbbk $ . Under mild restrictions on the characteristic of , we show that any G-module with good filtration also has as module for part centralizer nilpotent element x in its Lie algebra.

We obtain the decomposition of the tensor spacesl⊗k n as a module forsln , find an explicit formula for the multiplicities of its irreducible summands, and (when n ≥ 2k) describe the centralizer algebra C = Endsln (sl⊗k n ) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of C is given by the number...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type b A n?1. We give two constructions of this algebra. The rst construction realizes the algebra as a certain endomorphism algebra arising from an aane Hecke algebra of type b A r?1 , where n r. This generalizes the original q-Schur algebra as deened by Dipper and James, and the new algebra contains the ordinary ...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type A n−1. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of type A r−1 , where n ≥ r. This generalizes the original q-Schur algebra as defined by Dipper and James, and the new algebra contains the ordina...

The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a group such the centralizer of every nontrivial element torsion-free while infinite order We show either pro- p for some prime or procyclic ( Theorem 1.1 ). same conclusion holds 1.2 ); moreover, if not , then has finite rank.