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arXiv · 2203.14548

Average order in wreath products

Supravat Sarkar
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Abstract

We obtain an exact formula for the average order of elements of a wreath product of two finite groups. Then focussing our attention on $p$-groups for primes $p$, we give an estimate for the average order of a wreath product $A\wr B$ in terms of maximum order of elements of $A$ and average order of $B$ and an exact formula for the distribution of orders of elements of $A\wr B.$ Finally, we show how wreath products can be used to find several rational numbers which are limits of average orders of a sequence of $p$-groups with cardinalities going to infinity.

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Supravat Sarkar. 2022-03-28. Average order in wreath products. https://arxiv.org/abs/2203.14548

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