Average order in regular wreath products

Document Type : Research Paper

Author

Mathematics Ph.D. student in Princeton University, USA

Abstract

We obtain an exact formula for the average order of elements of regular wreath product of two finite groups. Then focussing our attention on $p$-groups for primes $p$, we give an estimate for the verage 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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References

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[6] M. S. Lazorec and M. Tarnauceanu , On the average order of a finite group, J. Pure Appl. Algebra, 227 (2023) 9 pp.

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History

  • Receive Date: 30 November 2022
  • Revise Date: 09 September 2023
  • Accept Date: 16 September 2023
  • Published Online: 01 June 2024

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