有限群元素的对称表示
Symmetric representation of the elements of finite groups
摘要：
许多有限群，包括所有有限非交换单群，都可以由对合对称生成。本文给出了有限群的元素的对称表示和对称表示元素的置换表示的变换算法。特别地，我们表示组$U_3(3) : 2$的元素，其中$U_3(3)$是在字段$\mathbb{F}_3$中具有条目的$3 \times 3$矩阵的射影特殊酉群，作为来自一般射影线性群$PGL_2(7)$的14个字母的置换，后跟14个对合对称生成元中长度最多为2的字。
英文摘要：
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically represented elements in terms of their permutation representation. In particular, we represent elements of the group $U_3(3) : 2$, where $U_3(3)$ is the projective special unitary group of $3 \times 3$ matrices with entries in the field $\mathbb{F}_3$, as a permutation on fourteen letters from the projective general linear group $PGL_2(7)$, followed by a word of length at most two in the fourteen involutory symmetric generators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
