A proper subgroup M of a finite group G is called a CCsubgroup of G if the centralizer CG(m) of every m ∈ M = M \ {1} is contained in M . Such finite groups had been partially classified by S.Williams, A. S.Kondrat’iev, N. Iiyori and H.Yamaki, M. Suzuki, W.Feit and J. G.Thompson, M.Herzog, Z.Arad, D.Chillag and others. In [6] the present authors, having taken all this work into account, classif...

Let n, r be integers 1 and let V be a vector space of dimension n over C. Classically, we have natural commuting actions of the general linear group GL(V) and the symmetric group Sr on the tensor space V⊗r, and both actions satisfy the so-called Weyl reciprocity [W] (or the double centralizer property), which has been used by Schur and Weyl to link representations of Sr with representations of ...

We introduce the multiset partition algebra, ${\rm M\!P}_{r,k}(x)$, that has bases elements indexed by partitions, where $x$ is an indeterminate and $r$ $k$ are non-negative integers. This algebra can be realized as a diagram generalizes algebra. When integer greater or equal to $2r$, we show M\!P}_{r,k}(x)$ isomorphic centralizer of symmetric group, $S_n$, acting on polynomial ring variables $...

In this paper we study some combinatorial aspects of the singular Artin monoids. Firstly, we show that a singular Artin monoid SA can be presented as a semidirect product of a graph monoid with its associated Artin group A. Such a decomposition implies that a singular Artin monoid embeds in a group. Secondly, we give a solution to the word problem for the FC type singular Artin monoids. Afterwa...

Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan

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...

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].

We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation...

We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation...