Some simple biset functors

2021/05/15 by Bouc, Serge
#18B99 #19A22 #20J15 #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2105.07234

Abstract

Let p be a prime number, let H be a finite p-group, and let \mathbbF be a field of characteristic 0, considered as a trivial \mathbbF Out(H)-module. The main result of this paper gives the dimension of the evaluation S_H,\mathbbF(G) of the simple biset functor S_H,\mathbbF at an arbitrary finite group G. A closely related result is proved in the last section: for each prime number p, a Green biset functor E_p is introduced, as a specific quotient of the Burnside functor, and it is shown that the evaluation E_p(G) is a free abelian group of rank equal to the number of conjugacy classes of p-elementary subgroups of G.

Related

• p-Biset Functor of Monomial Burnside Rings
• Simple biset functors and double Burnside rings
• On fibred biset functors with fibres of order prime and four
• The functor of units of Burnside rings for p-groups
• p-Bifree biset functors