Group algebras with units satisfying an Engel identity
β Scribed by David M. Riley
- Publisher
- Springer Milan
- Year
- 2000
- Tongue
- Italian
- Weight
- 33 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0009-725X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let R = denote the group of units of an associative algebra R over an infinite field F. We prove that if R is unitarily generated by its nilpotent elements, then R = satisfies a group identity precisely when R satisfies a nonmatrix polynomial identity. As an application, we examine the group algebra
Let U be the group of units of the group algebra FG of a group G over a field F. Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a c