Related papers: Zassenhaus conjecture for $A_{6}$

In a previous paper, we stated and motivated counting conjectures for fusion systems that are purely local analogues of several local-to-global conjectures in the modular representation theory of finite groups. Here we verify some of these…

The three famous problems concerning units, zero-divisors and idempotents in group rings of torsion-free groups, commonly attributed to I. Kaplansky, have been around for more than 60 years and still remain open in characteristic zero. In…

We continue the construction of non-trivial vacua for gauge theories on the 3-torus, started in hep-th/9901154. Application of constructions based on twist in SU(N) with N > 2 produce more extra vacua in theories with exceptional groups. We…

This paper, together with a forthcoming paper by the author and Seitz, proves the Margulis-Platonov conjecture concerning the normal subgroup structure of algebraic groups over number fields, in the case of inner forms of anisotropic groups…

We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…

Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let $Z$ be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus…

In \cite[Problem 72]{Fuchs60} Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In a…

Kervaire conjecture that the weight of the free product of every non-trivial group and the infinite cyclic group is not one is confirmed by confirming Conjecture Z of a knot exterior.

We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable…

In this work, we compute the first and second Zagreb indices for the commuting conjugacy class graphs associated with finite groups. We identify multiple classes of finite groups whose commuting conjugacy class graphs are shown to satisfy…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…

Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence…

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of…

We show that for any compact Lie group $G$ with identity component $N$ and component group $W=G/N$, the category of free rational $G$-spectra is equivalent to the category of torsion modules over the twisted group ring $H^*(BN)[W]$. This…

We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group $SO(6)$. We provide evidence for these conjectures in the form of dimension formulas and explicit computations of…

For a finite group $G$ and $U: = U(\mathbb{Z}G)$, the group of units of the integral group ring of $G$, we study the implications of the structure of $G$ on the abelianization $U/U'$ of $U$. We pose questions on the connections between the…

For an arbitrary positive integer $n$ and a pair $(p, q)$ of coprime integers, consider $n$ copies of a torus $(p,q)$ knot placed parallel to each other on the surface of the corresponding auxiliary torus: we call this assembly a torus…

We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average $6$-torsion of the class group of quadratic number fields. We also prove Malle's conjecture for Galois…

We classify the Rauzy-Veech groups of all connected components of all strata of the moduli space of translation surfaces in absolute homology, showing, in particular, that they are commensurable to arithmetic lattices of symplectic groups.…

A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.