Fundamental groups and finite sheeted coverings

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...

Finite Groups with p-Sylow Coverings

finite groups with p-sylow coverings

Finite subnormal coverings of certain solvable groups

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

Normal coverings of finite symmetric and alternating groups

In this paper we investigate the minimum number of maximal subgroups Hi, i = 1 . . . k of the symmetric group Sn (or the alternating group An) such that each element in the group Sn (respectively An) lies in some conjugate of one of the Hi. We prove that this number lies between aφ(n) and bn for certain constants a, b, where φ(n) is the Euler phi-function, and we show that the number depends on...