We prove that a finite group acting by birational automorphisms of a nontrivial Severi-Brauer surface over a field of characteristic zero contains a normal abelian subgroup of index at most ##IMG## [http://ej.iop.org/images/1064-5616/211/3/466/MSB_211_3_466ieqn1.gif] {$3$} . Also, we find an explicit bound for the orders of such finite groups in the case when the base field contains all roots of ##IMG## [http://ej.iop.org/images/1064-5616/211/3/466/MSB_211_3_466ieqn2.gif] {$1$} . Bibliography: 25 titles.

中文翻译：

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Severi-Brauer曲面的双自同构

我们证明在特征零域上由非平凡Severi-Brauer曲面的双边同构性作用的有限群包含索引最多## IMG ##的正常阿贝尔群1064-5616 / 211/3/466 / MSB_211_3_466ieqn1.gif] {$ 3 $}。此外，在基本字段包含## IMG ##的所有根的情况下，我们找到了此类有限群阶的显式边界[http://ej.iop.org/images/1064-5616/211/3 /466/MSB_211_3_466ieqn2.gif] {$ 1 $}。参考书目：25种。