Related papers: On subgroups of finite classical groups with exact…

We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic group up to add extra formal diffeomorphisms. We show that this is the case for…

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M}…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Abstract polytopes are combinatorial structures with distinctive geometric, algebraic, or topological characteristics, that generalize (the face lattice of) traditional polyhedra, polytopes or tessellations. Most research has focused on…

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

We classify minimal transitive subsemigroups of the finitary inverse symmetric semigroup modulo the classification of minimal transitive subgroups of finite symmetric groups; and semitransitive subsemigroups of the finite inverse symmetric…

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that…

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.

In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of…

It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable…

Let X be a 2-sphere with n punctures. We classify all conjugacy classes of Zariski-dense representations $$\rho: \pi_1(X)\to SL_2(\mathbb{C})$$ with finite orbit under the mapping class group of X, such that the local monodromy at one or…

An abstract group $G$ is called totally $2$-closed if $H=H^{(2),\Omega}$ for any set $\Omega$ with $G\cong H\leq{\rm Sym}(\Omega)$, where $H^{(2),\Omega}$ is the largest subgroup of ${\rm Sym}(\Omega)$ whose orbits on $\Omega\times\Omega$…

We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic fields. We give an application of our results to computing…