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arXiv · 1611.06428

Conjugacy growth series for finitary wreath products

Madeline Locus
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Abstract

We examine the conjugacy growth series of all wreath products of the finitary permutation groups $\text{Sym}(X)$ and $\text{Alt}(X)$ for an infinite set $X$. We determine their asymptotics, and we characterize the limiting behavior between the $\text{Alt}(X)$ and $\text{Sym}(X)$ wreath products. In particular, their ratios form a limit if and only if the dimension of the symmetric wreath product is twice the dimension of the alternating wreath product.

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Madeline Locus. 2016-11-19. Conjugacy growth series for finitary wreath products. https://doi.org/10.1007/s40993-016-0070-6

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