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Let $m$ be a positive integer and let $Omega$ be a finite set. The $m$-closure of $Gle$Sym$(Omega)$ is the largest permutation group on $Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $Omega^m$. The exact formula for the $m$-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this $m$-closure to be included in the wreath product of the $m$-closures of the factors.
We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.
We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of finitely gene
We extend work of the first author and Khoussainov to show that being Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group. This adds to the list of known examples of Cayley automatic groups.
We prove a Littlewood-Richardson type formula for $(s_{lambda/mu},s_{ u/kappa})_{t^k,t}$, the pairing of two skew Schur functions in the MacDonald inner product at $q = t^k$ for positive integers $k$. This pairing counts graded decomposition numbers
It is an open problem whether definability in Propositional Dynamic Logic (PDL) on forests is decidable. Based on an algebraic characterization by Bojanczyk, et. al.,(2012) in terms of forest algebras, Straubing (2013) described an approach to PDL ba