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We examine the conjugacy growth series of all wreath products of the finitary permutation groups $$\text {Sym}(X)$$ Sym ( X ) and $$\text {Alt}(X)$$ Alt ( X ) for an infinite set X. We determine their asymptotics, and we characterize the limiting behavior between the $$\text {Alt}(X)$$ Alt ( X ) and $$\text {Sym}(X)$$ Sym ( X ) wreath products. In particular,...
In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of these series. We define a new family of conjugacy growth series for the finitary alternating wreath product that are related to sums of modular forms of integer and half-integral weights, the...
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