Average order in wreath products
Supravat Sarkar

TL;DR
This paper derives an exact formula for the average order of elements in wreath products of finite groups, with specific focus on $p$-groups, and explores applications to limits of average orders in sequences of $p$-groups.
Contribution
It provides a new exact formula for average element order in wreath products and analyzes their distribution, especially for $p$-groups, advancing understanding of their algebraic properties.
Findings
Exact formula for average order in wreath products.
Estimate for average order of wreath products of $p$-groups.
Distribution of element orders in wreath products.
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 -groups for primes , we give an estimate for the average order of a wreath product in terms of maximum order of elements of and average order of and an exact formula for the distribution of orders of elements of Finally, we show how wreath products can be used to find several rational numbers which are limits of average orders of a sequence of -groups with cardinalities going to infinity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Limits and Structures in Graph Theory · Graph theory and applications
