We determine the 2-fusion systems of J-component type in which centralizer some fully centralized involution has a maximal that is system U 3 ( ) .

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

Let G be a compact Lie group and p a fixed prime number. Recall that an elementary abelian p-group is an abelian group isomorphic to (Z/p) for some r. Jackowski and McClure showed in [10] how to decompose the classifying space BG at the prime p as a homotopy colimit of spaces of the form BCG(V ), where V is a nontrivial elementary abelian p-subgroup of G and CG(V ) is the centralizer of V in G ...

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

Given a field F , a scalar λ ∈ F and a matrix A ∈ F, the twisted centralizer code CF (A, λ) := {B ∈ F | AB − λBA = 0} is a linear code of length n. When A is cyclic and λ 6= 0 we prove that dimCF (A, λ) = deg(gcd(cA(t), λcA(λt))) where cA(t) denotes the characteristic polynomial of A. We also show how CF (A, λ) decomposes, and we estimate the probability that CF (A, λ) is nonzero when |F | is f...

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 uppe...