Related papers: The Cremona group and its subgroups

We show that for any $n\geq5$ there exist connected algebraic subgroups in the Cremona group $\mathrm{Bir}(\mathbb{P}^n)$ that are not contained in any maximal connected algebraic subgroup. Our approach exploits the existence of stably…

In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.

We survey different topologizations of the set $\mathcal{S}(G)$ of all closed subgroups of a topological group $G$ and demonstrate some applications in Topological Grous, Model Theory, Geometric Group Theory, Topological Dynamics.

In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].

Many groups with diverse convictions are interacting online. Interactions in online communities help people to engage each other and enhance understanding across groups. Online communities include multiple sub-communities whose members are…

In this paper we classify reflection subgroups of Euclidean Coxeter groups.

A general theoretical framework based on group-subgroup and group-supergroup relations is proposed to describe and to derive interpenetrating nets.

Some question about representations of $p$-adic groups are discussed.

The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.

We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.

We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of Chevalley groups; constructing p-groups…

We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano…

In this paper I classify, up to Cremona transformations, the Galois cover of the plane with Galois group of the form $\mathbb Z_2^r$.

This is a survey on Kawaguchi-Silverman conjecture.

In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.

This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

In this paper we study semigroups satisfying the identity $aba=ab$.

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.

We present an overview of computational methods for Bredon cohomology with a special focus on infinite groups