Covering the symmetric groups with proper subgroups

Finite Groups with p-Sylow Coverings

On the covering number of small symmetric groups and some sporadic simple groups

A set of proper subgroups is a covering for a group if its union is the whole group. The minimal number of subgroups needed to cover G is called the covering number of G, denoted by σ(G). Determining σ(G) is an open problem for many nonsolvable groups. For symmetric groups Sn, Maróti determined σ(Sn) for odd n with the exception of n = 9 and gave estimates for n even. In this paper we determine...

Subgroups of Infinite Symmetric Groups

This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...

Classifying fuzzy normal subgroups of finite groups

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.

On subgroups of topologized fundamental groups and generalized coverings

‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...