We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II(1), factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

The aim of this paper is to classify the finite nonsolvable groups in which every irreducible character of even degree vanishes on at most two conjugacy classes. As a corollary, it is shown that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class.

Solvability of the conjugacy problem for relatively hyperbolic groups was announced by Gromov [12]. Using the definition of Farb of a relatively hyperbolic group [9], we prove this assertion. We conclude that the conjugacy problem is solvable for the following two classes of groups: fundamental groups of complete, finite-volume, negatively curved manifolds, and finitely generated fully residual...

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

S. Gersten announced an algorithm that takes as input two finite sequences K →=(K 1 ,⋯,K N ) and ′ of conjugacy classes finitely generated subgroups F n outputs:

Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...