Outer plethysm, Burnside ring and \(\beta\)-rings (Q914828)

Let B(S) denote the graded ring given by \(B(S)=\oplus_{n\geq 0}B(\Sigma_ n)\), the sum of the Burnside rings of all the finite symmetric groups. The author introduces an outer plethysm operation into B(S) and verifies for it identities which are analogous to those satisfied by the outer plethysm on the representation ring \(R(S)=\oplus_{n\geq 0}R(\Sigma_ n)\).