Related papers: Finite simple groups of small essential dimension
This is the third one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups in odd dimension.
In this paper, we compute the essential $l$-dimension of the finite groups of classical Lie type for odd primes $l$ not equal to the defining prime, specifically the general linear groups, the symplectic groups, the orthogonal groups, and…
We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…
We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.
By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
We study the problem of deciding whether or not the image of an irreducible representation of the braid group $\B_3$ of degree $\leq 5$ has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm…
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.
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
It is shown that a finite group in which more than 3/4 of the elements are involutions must be an elementary abelian 2-group. A group in which exactly 3/4 of the elements are involutions is characterized as the direct product of the…
We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…
In this paper, we compute the essential $p$-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the…
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion…
The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…
Small covers arising from 3-dimensional simple polytopes are an interesting class of 3-manifolds. The fundamental group is a rigid invariant for wide classes of 3-manifolds, particularly for orientable Haken manifolds, which include…
Any simple pseudofinite group G is known to be isomorphic to a (twisted) Chevalley group over a pseudofinite field. This celebrated result mostly follows from the work of Wilson in 1995 and heavily relies on the classification of finite…
In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…