Related papers: Double cosets in free groups
In the present paper we consider biologically motivated reduction operations on double occurrence words. Then we define the nesting index of a double occurrence word to be the least number of reduction operations it takes for a word to be…
If a soluble group $G$ contains two finitely generated abelian subgroups $A,B$ such that the number of double cosets $AgB$ is finite, then $G$ is shown to be virtually polycyclic.
We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category.…
Recently it has been shown that all non-trivial closed permutation groups containing the automorphism group of the random poset are generated by two types of permutations: the first type are permutations turning the order upside down, and…
Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.
We introduce the factorization graph of a finite group and study its connectedness and forbidden structures. We characterize all finite groups with connected factorization graphs and classify those with connected bipartite factorization…
We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…
We construct and study various dual pairs between finite dimensional classical Lie groups and infinite dimensional Lie algebras in some Fock representations. The infinite dimensional Lie algebras here can be either a completed infinite rank…
We re-cast in a more combinatorial and computational form the foldings approach of John Stallings and pursue a detailed study of the subgroup structure of free groups. In particular, we introduce the notions of an "algebraic" and a "free"…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.
We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this…
In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
In this article, we study geometric properties of nilpotent groups. We find a geometric criterion for the word problem for the finitely generated free nilpotent groups. By geometric criterion, we mean a way to determine whether two words…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.
Let $F$ be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the $R_{\infty}$ property. Finally, we also show that…
We study the structure of two-sided vector spaces over a perfect field $K$. In particular, we give a complete characterization of isomorphism classes of simple two-sided vector spaces which are left finite-dimensional. Using this…