We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

We construct a hyperbolic group containing a finitely presented subgroup, which has infinitely many conjugacy classes of finite-order elements. We also use a version of Morse theory with high dimensional horizontal cells and use handle cancellation arguments to produce other examples of subgroups of CAT(0) groups with infinitely many conjugacy classes of finite-order elements.

Let G be a finite group and C(G) be the family of representative conjugacy classes of‎ ‎subgroups of G‎. ‎The matrix whose H,K-entry is the number of ‎fixed points of the set G/K under the action of H is called the‎ ‎table of marks of G where H,K run through all elements in‎ C(G)‎. Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...

Abstract. Let SL(2, q) be the group of 2× 2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of at least q − 1 distinct conjugacy classes of SL(2, q). On the other hand, if q > 3 is odd, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of a...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is proved that this measure agrees with a second measure on conjugacy classes of the Weyl group in...

Abstract Let