The normalizer of an element of a group is defined as the subgroup of all elements commuting with it; this subgroup is often also called the centralizer of the given element. In the second version [F-GM] the authors switched to the latter terminology, and we will also use the term “centralizer”. The conjecture was supported by a new algorithm for finding generators of a centralizer, suggested i...

Generically (for r + s ≥ n) the centralizer algebra for the action of GLn(C) on mixed tensor space (C n) ⊗r ⊗ ((C n) *) ⊗s is a certain subalgebra of the Brauer algebra, known as the walled (or rational) Brauer algebra. This paper studies a q-deformation, B n r,s (q), of the walled Brauer algebra and shows that the centralizer algebra for the action of the quantum group UR(gl n) on mixed tensor...

We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space ∆ ⊗⊗ k V . Here ∆ is the fundamental representation of Pin(N) and V is the natural (vector) representation of the orthogonal group O(N). We consider the centralizer algebra CPk = EndPin(N)(∆ ⊗⊗k V ) for Pin(N), the double covering group of O(N) and define...

Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the pro...

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.

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

In this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset the centralizer an involution in finite non-abelian simple group $G$ contains odd order element, unless $G=\text{PSL}(n,2)$ for $n\geq 4$. More precisely, show does not hold alternating $A_{8n}$ all 2$.

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...

Let G be a finite group having a normal p-subgroup N that contains its centralizer CG(N), and let R be a p-adic ring. It is shown that any finite p-group of units of augmentation one in RG which normalizes N is conjugate to a subgroup of G by a unit of RG, and if it centralizes N it is even contained in N .