Given an n×n matrix c over a unitary ring R, the centralizer of in full Mn(R) is called principal ring, denoted by Sn(c,R). We investigate its structure and prove: (1) If invertible with c-free point, or if R has no zero-divisors Jordan-similar all eigenvalues center then separable Frobenius extension Sn(c,R) sense Kasch. (2) integral domain matrix, cellular R-algebra Graham Lehrer. In particul...

for a finite group $g$‎, ‎let $cent(g)$ denote the set of centralizers of single elements of $g$‎. ‎in this note we prove that if $|g|leq frac{3}{2}|cent(g)|$ and $g$ is 2-nilpotent‎, ‎then $gcong s_3‎, ‎d_{10}$ or $s_3times s_3$‎. ‎this result gives a partial and positive answer to a conjecture raised by a‎. ‎r‎. ‎ashrafi [on finite groups with a given number of centralizers‎, ‎algebra‎ ‎collo...

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.