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## Finite groups of birational transformations

P. 413-437.

We survey new results on finite groups of birational transformations of algebraic varieties.

Publication based on the results of:

Prokhorov Y., / Cornell University. Series arXiv "math". 2021.

We survey new results on finite groups of birational transformations of algebraic varieties. ...

Added: November 25, 2021

Athens : The Hellenic Open University, 2013

The book contains the reports of the member of the congress from the different countres. They consider the idea of the symmety in the science and in the art. ...

Added: January 30, 2014

Perepechko A., Mathematical notes 2021 Vol. 110 No. 5 P. 732-737

Affine algebraic surfaces of Markov type of the form (Formula presented.) are studied. Their automorphism groups are found. ...

Added: October 28, 2022

Shramov K., / Cornell University. Series arXiv "math". 2020.

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero. ...

Added: August 19, 2020

Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups

Gavrilovich M., Archive for Mathematical Logic 2018

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms. ...

Added: October 19, 2018

Shramov K., / Cornell University. Series arXiv "math". 2019.

We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration. ...

Added: November 19, 2019

Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921

In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...

Added: October 4, 2021

Popov V. L., Doklady Mathematics 2018 Vol. 98 No. 2 P. 413-415

The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established. ...

Added: November 13, 2018

Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups

Gavrilovich M., / arxiv. Series math.GR "arxiv". 2017.

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms. ...

Added: July 20, 2017

Busjatskaja I., Monastyrsky M. I., , in : Symmetry: Art and Science. Special Issue for the Congress-Festival of ISIS-Symmetry. : Athens : The Hellenic Open University, 2013. P. 248-253.

The paper examines the significance of Platonic Solids in different parts of modern science. ...

Added: January 30, 2014

Gavrilovich M., / arxiv. Series arxiv "math.CT". 2017.

We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of ...

Added: July 21, 2017

Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135-168

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...

Added: September 7, 2021

Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591-612

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...

Added: September 8, 2021