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 wreath product 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 wreath product 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.