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...

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...