A basis for powers of the augmentation ideal (Q2731588)

Let \(\mathbb{Z} G\) be the integral group ring of a finite elementary Abelian \(p\)-group \(G\) and \(\Delta(G)\) be the augmentation ideal of \(\mathbb{Z} G\). Here, the author gives an inductive method for constructing a \(\mathbb{Z}\)-basis of the Abelian group \(\Delta^n(G)\). This result is applied to the problem of finding a presentation for \(\Delta^n(G)\), whenever \(G\) has exponent 2 or 3. For arbitrary primes \(p\), the result is obtained for \(1\leq n\leq 3\).