题号:14617    题型:解答题    来源:2024年丘成桐大学生数学竞赛(代数与数论类)-无答案
Let $G$ be a finite group.
(1) Let $K$ be a field. Show that $G$ has a finite-dimensional fait hful $K$-linear representation.
(2) Show that $G$ has a faithful one-dimensional complex repr esentation if and only if $G$ is cyclic.
(3) Assume moreover that $G$ is commutative. Let $n \geq 1$ be an integer. Show that $G$ has a faithful $n$-dimensional complex re presentation if and only if $G$ can be generated by $n$ elements.
(4) Classify all finite groups having a faithful 2-dimensional re al representation.
0 人点赞 纠错 ​ 17 次查看 ​ 我来讲解
答案:

解析:

答案与解析:
答案仅限会员可见 微信内自动登录手机登录微信扫码注册登录 点击我要 开通VIP