Computing Whitehead groups using genetic bases

We combine results about Whitehead groups of finite groups with results about genetic bases of finite p-groups to compute the Whitehead groups of some metacyclic p  -groups. Let CpnCpn denote a cyclic group of order pnpn for p an odd prime and n   a positive integer. We present a conjecture for the torsion part of the Whitehead group of Cpn×CpnCpn×Cpn and we show that torsion part of the Whitehead group of the semidirect product of Cpn−1Cpn−1 by CpCp is isomorphic to Cp(n−2)(p−1). The techniques we use can be applied to any abelian p-group and to many other p-groups for p odd.