Word maps with small image in simple groups
Group Theory
2012-06-07 v1
Abstract
We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are precisely the identity and a single equivalence class of elements of order 17. In the second part we construct words which have image consisting of the identity and a single equivalence class of elements in Alt(n) for all n for any equivalence class with support size at most 10.
Cite
@article{arxiv.1206.1206,
title = {Word maps with small image in simple groups},
author = {Matthew Levy},
journal= {arXiv preprint arXiv:1206.1206},
year = {2012}
}