Chirality and non-real elements in $G_2(q)$
Abstract
In this article, we determine the non-real elements--the ones that are not conjugate to their inverses--in the group $G = G_2(q)$ when $char(F_q)\neq 2,3$. We use this to show that this group is chiral; that is, there is a word w such that $w(G)\neq w(G)^{-1}$. We also show that most classical finite simple groups are achiral
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.15546
- arXiv:
- arXiv:2408.15546
- Bibcode:
- 2024arXiv240815546B
- Keywords:
-
- Mathematics - Group Theory;
- 20D05;
- 20F10
- E-Print:
- 13 pages. Keywords: Chirality, word maps, non-real elements, an exceptional group of Lie type G_2(q)