Abstract
We study the simple subfunctors of indecomposable projective Mackey functors for a p-group P. Unlike the case of group algebras, the Mackey algebra is not in general self-injective. Thus, the socle of an indecomposable projective functor is not in general simple. We first show that the simple subfunctors of a projective functor P H , k , where H ⩽ P , are indexed by the normalizer in H of a subgroup of H. We then study the socle of a specific projective Mackey functor, namely the Burnside functor B P , and we focus on the case where P is abelian. In particular, our study enables us to determine the socle of an indecomposable projective Mackey functor indexed by a cyclic p-group, an abelian p-group of rank 2 and an elementary abelian p-group of rank 3.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.