On the invariants of root subgroups of finite classical groups

• Published in: Український математичний журнал
• Date: 2013
• Main Authors: Jizhu Nan, Yufang Qin
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165719
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the invariants of root subgroups of finite classical groups / Jizhu Nan, Yufang Qin // Український математичний журнал. — 2013. — Т. 65, № 12. — С. 1636–1645. — Бібліогр.: 15 назв. — англ.

We show that invariant fields Fq(X1, . . . , Xn)G are purely transcendental over Fq if G are root subgroups of finite classical groups. The key step is to find good similar groups of our groups. Moreover, the invariant rings of the root subgroups of special linear groups are shown to be polynomial...