Related papers: Essential Dimension of Small Finite Groups

In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders and superexpanders. This also provides a strong coarse…

We compute the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the…

In this paper, the author introduces the concept and basic properties of finite (commutative) hyperfields. Also, the author shows that, up to isomorphism, there are exactly 2 hyperfields of order 2; 5 hyperfields of order 3; 7 hyperfields…

EI categories can be thought of as amalgams of finite posets and finite groups and therefore the associated algebras are built up from incidence algebras and group algebras of finite groups. For this particular class of algebras we present…

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every…

We consider the structure of a finite groups having a normal series whose factors have bicyclic Sylow subgroups. In particular, we investigated groups of odd order and $A_4$-free groups with this property. Exact estimations of the derived…

We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.

In this note we study the finite groups whose subgroup lattices are dismantlable.

We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…

In this note, we study the finite groups whose Chermak-Delgado measure has exactly two values. They determine an interesting class of $p$-groups containing cyclic groups of prime order and extraspecial $p$-groups.

Let $U_n(q)$ be the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. In this paper, we present constructions of large degree ordinary irreducible representations of $U_n(q)$ where $n\geq 7$, and then…

We determine the fundamental group of period domains over finite fields.

In this article we prove results about finite soluble groups that act with fixity 2 or 3.

This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $\Gamma$ and $\Lambda$. It will suffice to take a finite quotient which is abelian, dihedral, a…

We produce a short and elementary algorithm to compute an upper bound for the canonical dimension of a spit semisimple linear algebraic group. Using this algorithm we confirm previously known bounds by Karpenko and Devyatov as well as we…

We investigate a degree 5 invariant of groups of type E8 and give its applications to the structure of finite subgroups in algebraic groups.

We show that the analog category of a finite group is essentially proportional to the size of its largest Sylow subgroup. We conclude that the universal upper bound given by the order of the group is very far from optimal.

We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.

We introduce the concept of quantifying the extent to which a finitely generated group is residually finite. The quantification is carried out for some examples including free groups, the first Grigorchuk group, finitely generated nilpotent…

We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group.