手性与$G_2(q)$中的非实数元素

arXiv - MATH - Group Theory Pub Date : 2024-08-28 DOI:arxiv-2408.15546

Sushil Bhunia, Amit Kulshrestha, Anupam Singh

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引用次数: 0

摘要

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

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

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arXiv - MATH - Group Theory

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