Periodicity of Adams operations on the Green ring of a finite group

الأصل · EN

The Adams operations ψΛⁿ and ψₛⁿ on the Green ring of a group G over a field K provide a framework for the study of the exterior powers and symmetric powers of KG-modules. When G is finite and K has prime characteristic p we show that ψΛⁿ and ψₛⁿ are periodic in n if and only if the Sylow p-subgroups of G are cyclic. In the case where G is a cyclic p-group we find the minimum periods and use recent work of Symonds to express ψₛⁿ in terms of ψΛⁿ.