Chirality and non-real elements in $G_2(q)$

Sushil Bhunia; Amit Kulshrestha; Anupam Singh

Chirality and non-real elements in $G_2(q)$

Group Theory 2024-08-29 v1

Authors: Sushil Bhunia , Amit Kulshrestha , Anupam Singh

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

Cite

@article{arxiv.2408.15546,
  title  = {Chirality and non-real elements in $G_2(q)$},
  author = {Sushil Bhunia and Amit Kulshrestha and Anupam Singh},
  journal= {arXiv preprint arXiv:2408.15546},
  year   = {2024}
}

Comments

13 pages. Keywords: Chirality, word maps, non-real elements, an exceptional group of Lie type G_2(q)

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