Free subgroups of one-relator relative presentations
Abstract
Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\x11,...,xn1\. It is proved that for n2 the group \~G=<G,x1,x2,...,xn | w=1> always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x1 in w is one). Some generalisations of these results are discussed.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.