English

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.

Keywords

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}
}
R2 v1 2026-06-21T21:15:02.118Z