Units and class-groups in integral elementary Abelian group rings
Assume A to be an elementary abelian p-group with p odd. The group of units in \({\mathbb{Z}}A\) having augmentation 1 and being invariant under the canonical involution on \({\mathbb{Z}}A\) is closely related to the product of the corresponding unit groups of \({\mathbb{Z}}C\), C varying over all cyclic subgroups, and also of \({\mathbb{Z}}K\), K varying over all cyclic factor groups. The main result of the paper is concerned with those units of \({\mathbb{Z}}A\) which cannot be written as products of ``cyclic'' units; there are no such, if p is regular, but for irregular, semi-regular p such units exist.
scientific article; zbMATH DE number 4021376
scientific article