Related papers: Odd length for even hyperoctahedral groups and sig…

A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent $n \gg 1$ is given in the following form. Let $Q$ be a group of odd exponent $n > 2^{48}$ and $\mathcal G$ be an HNN-extension of $Q$. If $A…

We deal with two forms of the "uniqueness cases" in the classification of large simple $K^*$-groups of finite Morley rank of odd type, where large means the $m_2(G)$ at least three. This substantially extends results known for even larger…

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…

We study generating functions for the number of even (odd) permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function…

We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie group there is a maximum equivalence class of length…

It is shown that the characteristic vector field associated to a first order PDE has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian the given PDE. It is considered under which…

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 consider a generalization of the fundamental theorem of finitely generated abelian groups for some non-abelian groups, which is called OGS. First, we consider the dihedral group, which is a non-abelian extension of an abelian group by an…

We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…

We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word…

The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\mathbb{Z}_r \wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length…

We consider the set of affine permutations that avoid a fixed permutation pattern. Crites has given a simple characterization for when this set is infinite. We find the generating series for this set using the Coxeter length statistic and…

We consider locally compact subgroups $H$ of the full isometry group $\mathrm{Isom}(\mathbb{E}^n)$ of Euclidean $n$-space which respect the splitting into an orthogonal and a translation subgroup. We prove that the conjugator length…

In this paper we study generating functions resembling the rank of strongly unimodal sequences. We give combinatorial interpretations, identities in terms of mock modular forms, asymptotics, and a parity result. Our functions imitate a…

We prove very general formulae for the generating series of (Hodge) genera of symmetric products with coefficients, which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical…

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…

Introduced by Solomon in his 1976 paper, the descent algebra of a finite Coxeter group received significant attention over the past decades. As proved by Gessel, in the case of the symmetric group its structure constants give the…

A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…

All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…

In this paper, we deal with reversing and extended symmetries of shifts generated by bijective substitutions. We provide equivalent conditions for a permutation on the alphabet to generate a reversing/extended symmetry, and algorithms how…