Free Subgroups of Free Complete Products

Fixed Subgroups of Endomorphisms of Free Products

Let G = ∗ i=1 Gi and let φ be a symmetric endomorphism of G. If φ is a monomorphism or if G is a finitely generated residually finite group, then the fixed subgroup Fix(φ) = {g ∈ G : φ(g) = g} of φ has Kurosh rank at most n.

Frobenius Subgroups of Free Profinite Products

We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of free profinite products.

Near Frattini Subgroups of Certain Generalized Free Products of Groups

Let G = A ∗H B be the generalized free product of the groups A and B with the amalgamated subgroup H. Also, let λ(G) and ψ(G) represent the lower near Frattini subgroup of G and the near Frattini subgroup of G respectively. We show that G is ψ−free provided: (i) G is any ordinary free product of groups; (ii) G = A ∗H B and there exists an element c in G\H such thatH ∩H = 1; (iii) G = A ∗H B and...

Prosolvable Subgroups of Free Products of Profinite Groups

Subgroups of Free Topological Groups and Free Topological Products of Topological Groups

Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9]. However we might expect a subgroup theorem when a continuous Schreier transversal exists, and we give such a result in th...