@article{SchreierDieUD,
title={Die Untergruppen der freien Gruppen},
author={Otto Schreier},
journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
volume={5},
pages={161-183}
}

Following partially a suggestion by Pyber, we prove that the diameter of a product of non-abelian finite simple groups is bounded linearly by the maximum diameter of its factors. For completeness, we… Expand

We discuss in the context of finite extensions two classical theorems of Takahasi and Howson on subgroups of free groups. We provide bounds for the rank of the intersection of subgroups within… Expand

The residual torsion-free nilpotence of the commutator subgroup of a knot group has proven to be an important property with applications to ribbon concordance and bi-orderability. In a lecture,… Expand

A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p, there exists a group G# and an epimorphism φ : G# −→ G whose kernel is an elementary abelian p-group… Expand

This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the… Expand

We prove that the word problem for the free product with amalgamation S *UT of monoids can be undecidable, even when S and T are finitely presented monoids with word problems that are decidable in… Expand

In "Subgroups of free profinite groups and large subfields of Q" (Israel J. Math. 39 (1981), no. 1-2, pages 25-45; MR 617288) A. Lubotzky and L. van den Dries raise the question whether a finitely… Expand

Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$… Expand