Big Free Groups are Almost Free
Group Theory
2015-06-12 v2
Abstract
It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement is in fact a simple corollary of the more general result proven below on the extendability of homomorphisms from subgroups (of a certain kind) of the big free group to a compact topological group.
Cite
@article{arxiv.1312.4750,
title = {Big Free Groups are Almost Free},
author = {Tamer Tlas},
journal= {arXiv preprint arXiv:1312.4750},
year = {2015}
}
Comments
10 pages, several arguments expanded with no change in the results, one reference added