The centralizer C(w) of an elliptic element w in a Weyl group has a natural symplectic representation on the group of w-coinvariants in the root lattice. We give the basic properties of this representation, along with applications to p-adic groups—classifying maximal tori and computing inducing data in L-packets—as well as to elucidating the structure of the centralizer C(w) itself. We give the...

The following basic results on infinite locally finite subgroups of a free m-generŽ . 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 29, are obtained: A clear complete description of all infinite groups that Ž . Ž . are embeddable in B m, n as maximal locally finite subgroups is given. Any Ž . infinite locally finite subgroup L of B m, n is contained...

For a monoid M of k-valued unary operations, the centralizer M∗ is the clone consisting of all k-valued multi-variable operations which commute with every operation in M . First we give a sufficient condition for a monoid M to have the least clone as its centralizer. Then using this condition we determine centralizers of all monoids containing the symmetric group. AMS Mathematics Subject Classi...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...

A group G is said to be n-centralizer if its number of element centralizers $$\mid {{\,\mathrm{Cent}\,}}(G)\mid =n$$ , an F-group every non-central centralizer contains no other and a CA-group all are abelian. For any non-abelian G, we prove that \frac{G}{Z(G)}\mid \le (n-2)^2$$ $$n 12$$ 2(n-4)^{{log}_2^{(n-4)}}$$ otherwise, which improves earlier result. We arbitrary F-group, then gcd $$(n-2, ...

We prove that the centralizer of a Coxeter element in an irreducible group is cyclic generated by element.

We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik’s commuting algebra of difference operators via an analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are defined and realized as solutions to the system of basic hypergeometric difference equatio...

BACKGROUND AND PURPOSE A proximal stem centralizer may be beneficial regarding cementing pressures, cement penetration, and stem alignment. We measured these parameters when cementing a mat-surfaced femoral component with and without the use of a proximal stem centralizer. MATERIAL AND METHODS 8 femoral prostheses with proximal centralizers and 8 femoral prostheses without proximal centralize...

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another application we giv...