Том 71
№ 11

All Issues

Nan Jizhu

Articles: 1
Article (English)

On the Invariants of Root Subgroups of Finite Classical Groups

Nan Jizhu, Qin Yufang

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 12. - pp. 1636–1645

We show that the invariant fields F q (X 1 , . . . ,X n ) G are purely transcendental over F q 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 rings and their corresponding Poincaré series are presented.