Growth sequences of finite groups V
D. Meier, James Wiegold · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1981
Abstract A short and easy proof that the minimum number of generators of the nth direct power of a non-trival finite group of order s having automorphism group of order a is more than logsn + logsa, n > 1. On the other hand, for non-abelian simple G and large n, d(Gn) is within 1 + e of logsn + logsa.