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Article

Торы в группах Кремоны

We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups.
We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the Linearization Problem generalizing to disconnected groups Bialynicki-Birula's results  of 1966--67. We prove ``fusion theorems'' for  n-dimensional tori in the affine and in the special affine Cremona groups of rank  n. In the final section we introduce and discuss  the notions of Jordan decomposition and torsion prime numbers for the Cremona groups.