average order in regular wreath products

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 average order of a wreath product a ≀ 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 ≀ 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.