Related papers: Combinatorial Burnside groups
We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…
We consider the Clifford algebra and the Clifford group associated with any quadratic module, degenerate or not, over an arbitrary commutative ring with 1. We determine some of the important subalgebras of the Clifford algebra under some…
A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred…
Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the…
We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method is very flexible and can also be used to study (partially) periodic quotients of any group which admits an action on a hyperbolic…
We consider geometric invariant theory for \emph{graded additive groups}, groups of the form $\mathbb{G}_a^r\rtimes_w\mathbb{G}_m$ such that the $\mathbb{G}_m$-action on $\mathbb{G}_a^r$ is a scalar multiplication with weight…
We show that first-order formulae are concise in acylindrically hyperbolic groups and certain extensions thereof. We study further classes of groups, including Burnside groups, icc groups, groups with the `Big Powers' condition, torus knot…
Dendriform algebras are certain associative algebras whose product splits into two binary operations and the associativity splits into three new identities. In this paper, we study finite group actions on dendriform algebras. We define…
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N dimensions. The action associated to the bicrossproduct structure allows to obtain a…
We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
For a finite abelian group $G$, we compute the $G$-equivariant formal group law corresponding to the $G$-equivariant complex cobordism spectrum with its canonical complex orientation.
A cluster algebra is an algebraic structure generated by operations of a quiver (a directed graph) called the mutations and their associated simple birational mappings. By using a graph-combinatorial approach, we present a systematic way to…
A finite subgroup of $GL(n,\mathbb C)$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniform combinatorial model is constructed for all…
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these…
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.