R_C is not separable over Z; RB_G and RB(G) are separable over R iff |G| is invertible in R.
Bouc.Biset functors for finite groups
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On the separability of some Green biset functors
R_C is not separable over Z; RB_G and RB(G) are separable over R iff |G| is invertible in R.