Which alternating and symmetric groups are unit groups?
Rings and Algebras
2015-02-02 v1 Group Theory
Representation Theory
Abstract
We prove there is no ring with unit group isomorphic to S_n for n \geq 5 and that there is no ring with unit group isomorphic to A_n for n \geq 5, n \neq 8. We give examples of rings with unit groups isomorphic to S_1, S_2, S_3, S_4, A_1, A_2, A_3, A_4, and A_8. We expect our methods to work similarly for other groups with trivial center; in particular, we plan to consider other simple groups in later work.
Cite
@article{arxiv.1304.0143,
title = {Which alternating and symmetric groups are unit groups?},
author = {Christopher Davis and Tommy Occhipinti},
journal= {arXiv preprint arXiv:1304.0143},
year = {2015}
}
Comments
10 pages