The Artin-Hasse power series and p-adic group rings
Let p be an odd prime and \({\mathcal A}\) a finite abelian \(p\)-group. Let \({\mathbb{Z}}_{p}{\mathcal A}\) be the \(p\)-adic group ring of \({\mathcal A}\) and \({\mathcal E}({\mathcal T})\) the well known \(p\)-adically integral power series exp(\(\sum^{\infty}_{n=0}p^{-n}{\mathcal T}^{p^{n}})\). It is shown that the multiplicative group of \({\mathbb{Z}}_{p}{\mathcal A}\) formed by \(\{1+\sum_{z\in {\mathcal A}}a_{z}(z-2+z^{-1})|\) \(a_{z}\in {\mathbb{Z}}_{p}\}\) has the \({\mathbb{Z}}_{p}\)-basis \(\{\) \({\mathcal E}(z-2+z^{- 1}|\) \(1\neq z\in {\mathcal A}\}\).
scientific article; zbMATH DE number 4208359