Ideals of some Green biset functors
Abstract
In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M Cgroup, this definition generalizes that of a Bgroup, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M Cgroups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M Cgroups of A.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.17053
 arXiv:
 arXiv:2402.17053
 Bibcode:
 2024arXiv240217053C
 Keywords:

 Mathematics  Group Theory;
 16Y99;
 18D99;
 20J15