On schur rings over cyclic groups

In this paper, we introduce the notion of wedge product of Schur rings. We show that for any nontrivial Schur ringS over a cyclic groupG, if there is a subgroupH such that Σ _g ε _H g Σ _g∈H g ∉S, thenS is either a dot product or wedge product for some Schur rings over smaller cyclic groups.     

On the direct product of fuzzy topological groups

The connections between some countability properties of a topological space (X, $\text{T}$) and its generated fuzzy topological space (X, ω($\text{T}$)) are investigated.     

On schur rings of group rings of finite groups

Schur rings are rings associated to certain partitions of finite groups. They were introduced for applications in representation theory, cfr. [3][4].

The algebric structure of these rings has not been studied in depth. In this paper we determine explicit structure constants for Schur rings, we derive conditions for separability and we compute the centre. These results seem to be new even over fields.     

Pronormal subgroups of a direct product of groups

We give criteria to characterize abnormal, pronormal and locally pronormal subgroups of a direct product of two finite groups $A\times B$, under hypotheses of solvability for at least one of the factors, either A or B.     

FC-Groups whose central factor group can be embedded in a direct product of finite groups

We consider the question of whether an FC-group G in which the derived subgroup [G, G] is a subgroup of a direct product of finite groups must have its central factor group G/Z(G) also embeddable in a direct product of finite groups.     

On fundamental groups of quotient spaces

In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf spaces in general.     

The regular representation of restricted direct product groups

The regular representation of a restricted direct product of locally compact groups is analyzed. Examples of such groups for which the regular representations generate various type III infinite tensor product factors are constructed. Other related phenomena are considered, with examples.