Free products in the unit group of the integral group ring of a finite group

Let G be a finite group and let p be a prime. We continue the search for generic constructions of free products and free monoids in the unit group U(ZG) of the integral group ring ZG. For a nilpotent group G with a non-central element g of order p, explicit generic constructions are given of two periodic units b ₁ and b ₂ in U(ZG) such that 〈b ₁, b ₂〉 = 〈b ₁ 〉 ⋆ 〈b ₂〉 ≌ Z _p ⋆ Z _p, a free product of two cyclic groups of prime order. Moreover, if G is nilpotent of class 2 and g has order p ⁿ, then also concrete generators for free products Z _pk ⋆ Z _p ^m are constructed (with 1 ≤ k, m ≤ n). As an application, for finite nilpotent groups, we obtain earlier results of Marciniak-Sehgal and GonçalvesPassman. Further, for an arbitrary finite group G we give generic constructions of free monoids in U(ZG) that generate an infinite solvable subgroup.