In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

(A) We study in this paper topological properties of conjugacy classes in Polish groups. There are two questions which we are particularly interested in. First, does a Polish group G have a dense conjugacy class? This is equivalent (see, e.g., Kechris [95, 8.47]) to the following generic ergodicity property of G: Every conjugacy invariant subset A ⊆ G with the Baire property (e.g., a Borel set)...

1 2 3 Let T be a rooted tree and Iso(T ) be the group of its isometries. We study closed subgroups G of Iso(T ) with respect to the number of conjugacy classes of Iso(T ) having representatives in G.

Let G be a co-compact Fuchsian group. As such, it acts discontinuously on the hyperbolic plane H and the quotient is a closed hyperbolic 2-orbifold. The structure theory for co-compact Fuchsian groups yields a canonical presentation for such groups. This information is described by the signature s s g ; m , . . . , m 1 Ž . Ž . 1 r where g is the genus of the base surface of the quotient 2-orbif...

Suppose $G$ is a connected complex semisimple group and $W$ its Weyl group. The lifting of an element to semisimple. This induces well-defined map from the set elliptic conjugacy classes $G$. In this paper, we give uniform algorithm compute map. We also consider twisted case.

In this paper we analyze the structure of some sets of non-commutative moments of elements in a finite von Neumann algebra M . If the fundamental group of M is R+\{0}, then the moment sets are convex, and if M is isomorphic to M ⊗M , then the sets are closed under pointwise multiplication. We introduce a class of discrete groups that we call hyperlinear. These are the discrete subgroups (with i...

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...