Related papers: Realizing fusion systems inside finite groups

In this paper we prove that every finite group $G$ can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces $X$. Moreover, $X$ can be chosen to be the rationalization of an inflexible compact simply…

We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…

We study group models for fusion systems and construct homology decompositions for the models of Robinson and Leary-Stancu type.

It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following…

We prove that every finite subgroup of $GL_{2}(\mathbb{R})$ can be realized as the Veech group of some translation surface.

In this paper we study the cellularization of classifying spaces of saturated fusion systems with respect to classifying spaces of finite p-groups. We give explicit algebraic criteria to decide when a classifying space is cellular.…

We introduce and study the new notion of an {\em exact factorization} $\mathcal{B}=\mathcal{A}\bullet \mathcal{C}$ of a fusion category $\mathcal{B}$ into a product of two fusion subcategories $\mathcal{A},\mathcal{C}\subseteq \mathcal{B}$…

For any prime $p$ and $S$ a $p$-group isomorphic to a Sylow $p$-subgroup of a rank $2$ simple group of Lie type in characteristic $p$, we determine all saturated fusion systems supported on $S$ up to isomorphism.

Given a saturated fusion system $\mathcal{F}$ over a finite $p$-group $S$, we provide criteria to determine when uniqueness of factorization into irreducible $\mathcal{F}$--invariant representations holds. We use them to prove uniqueness of…

We show that every saturated fusion system $\mathcal{F}$ has a unique minimal $\mathcal{F}$-characteristic biset $\Lambda_\mathcal{F}$. We examine the relationship of $\Lambda_\mathcal{F}$ with other concepts in $p$-local finite group…

In the paper we complete the classification of Carter subgroups in finite almost simple groups. In particular, we prove that Carter subgroups of every finite almost simple group are conjugate. Togeather with previous results by author and…

We prove there exist infinitely many inequivalent fusion categories whose Grothendieck rings do not admit any pseudounitary categorifications.

In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.

We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.

Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…

We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine…

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

This is the third and last of three papers containing the complete proof that all finitely presented groups are QSF.