Related papers: Probabilistic aspects of ZM-groups

We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a…

In this article we give a classification of the sub-groups in PSL(2,Z) and of the conjugacy classes of these sub-groups by the mean of an combinatorial invariant: some trivalent diagrams (dotted or not). We give explicit formulae enabling…

We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of…

We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy…

We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\frac{1}{3}]$, answering a question of Cameron, and that the number of those…

We show that the probability for a finitely generated subgroup of the modular group, of size $n$, to be almost malnormal or non-parabolic, tends to 0 as $n$ tends to infinity -- where the notion of the size of a subgroup is based on a…

In a paper by the first author it was shown that for certain arithmetical results on conjugacy class sizes it is enough to only consider the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only…

We obtain a series of new results on the problem of irreducibility of commuting varieties associated with symmetric pairs or, in other words, $Z_2$-graded simple Lie algebras. In particular, we present many examples of reducible commuting…

Recently, two first authors have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x\wedge y=1$ in the exterior square $G\wedge G$ of $G$. Research on this probability…

A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…

We compute the cohomology of the stack M_1 with coefficients in Z[1/2], and in low degrees with coefficients in Z. Cohomology classes on M_1 give rise to characteristic classes, cohomological invariants of families of curves of genus one.…

Let $ G $ be a cyclic group, in this paper, we study the Herbrand quotient and $ 1-$th cohomology group on finitely generated $ G-$modules in some cases. When $ G $ is of order $ 2, $ the order of the cohomology group is explicitly related…

The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…

Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…

We prove a formula connecting the number of unipotent conjugacy classes in a maximal parabolic subgroup of a finite general linear group with the numbers of unipotent conjugacy classes in various parabolic subgroups in smaller dimensions.…

The full lattices in a finite dimensional commutative ${\mathbb Q}$-algebra form a commutative semigroup. In the case of an algebraic number field the top part of a certain quotient semigroup is the class group. For a separable algebra some…

We determine the eigenvalues with multiplicity of each element of an alternating group in any irreducible representation. This is equivalent to determining the decomposition of cyclic representations of alternating groups into irreducibles.…

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n…