The functor of units of Burnside rings for p-groups
type: Dataset
description: In this note I describe the structure of the biset functor $B^\times$ sending a $p$-group $P$ to the group of units of its Burnside ring $B(P)$. In particular, I show that $B^\times$ is a rational biset functor. It follows that if $P$ is a $p$-group, the structure of $B^\times(P)$ can be read from a genetic basis of $P$~: the group $B^\times(P)$ is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational irreducible representations of~$P$ whose type is trivial, cyclic of order 2, or dihedral.
landing page: https://hal.science/hal-00087819
keyword: 19a22--16u60
keyword: biset-functor
keyword: burnside-ring
keyword: infoeu-reposemanticspreprint
keyword: mathmath-grmathematics-mathgroup-theory-mathgr
keyword: preprints-working-papers-
keyword: unit
issued: 2026-05-09T05:11:40.969848
modified: 2026-05-09T05:11:40.969853
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

The functor of units of Burnside rings for p-groups
type: Distribution
format: HTML
access URL: https://hal.science/hal-00087819
issued: 2026-05-09T05:11:40.974677
modified: 2026-05-09T05:11:40.961938