The closures of wreath products in product action

2021/07/10 by Ponomarenko, I., Vasil'ev, A. V.
#20B10 20B25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2107.04783

Abstract

Let m be a positive integer and let Ω be a finite set. The m-closure of G≤Sym(Ω) is the largest permutation group on Ω having the same orbits as G in its induced action on the Cartesian product Ω^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.

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