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

Sushil Bhunia, Amit Kulshrestha, Anupam Singh
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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
手性与$G_2(q)$中的非实数元素
在这篇文章中,我们确定了当 $char(F_q)\neq2,3$ 时,$G = G_2(q)$ 群中的非实数元素--即与它们的反函数不共轭的元素。我们利用这一点来证明这个群是手性的;也就是说,有一个词 wsuch $w(G)\neq w(G)^{-1}$。我们还证明了大多数经典有限简单群是无手性的
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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