Related papers: On generating sets of infinite symmetric group

We prove that if G is a sufficiently large finite almost simple group of Lie type, then given a fixed nontrivial element x in G and a coset of G modulo its socle, the probability that x and a random element of the coset generate a subgroup…

We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…

We show that the standard generating set of a Coxeter group is of minimal cardinality provided that the non-diagonal entries of the Coxeter matrix are sufficiently large.

It was conjectured in [KLS14] that for arithmetic groups, Invariable Generation is equivalent to the Congruence Subgroup Property. In view of the famous Serre conjecture this would imply that higher rank arithmetic groups are invariably…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established

We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated.

In [3] is was shown that for any group $G$ whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup $H\leq G$ with index $[G:H]\geq rank(G)$, one can always find a left-right transversal of $H$ which…

Let $G$ be a group. A subset $D$ of $G$ is a determining set of $G$, if every automorphism of $G$ is uniquely determined by its action on $D$. The determining number of $G$, denoted by $\alpha(G)$, is the cardinality of a smallest…

The rank of a point-line geometry G is usually defined as the generating rank of G, namely the minimal cardinality of a generating set. However, when the subspace lattice of G satisfies the Exchange Property we can also try a different…

We give a filtration of the unoriented cobordism ring using the infinite symplectic group, with polynomial generators given one at a time. The generating manifolds are also constructed using the cup construction.

Although degree bounds and algorithms for the generators of various invariant rings have been known for decades, little is known about the cardinality of minimal generating sets. Estimates of such would provide lower bounds for the runtime…

This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Grigorchuk.

The category of matchings between finite sets extends to the category of cobordisms of signed sets. A chain of cobordisms that starts and ends with unsigned sets A and B yields a matching from A to B. This is a convenient way to package the…

We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…

We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…

Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…

A subset $S$ of a group $G$ invariably generates $G$ if, when each element of $S$ is replaced by an arbitrary conjugate, the resulting set generates $G.$ An invariable generating set $X$ of $G$ is called minimal if no proper subset of $X$…

We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question…