Units of Burnside rings of elementary abelian 2-groups (Q5936183)

For a finite group \(G\), let \(S(G)\) be the set of \(G\)-isomorphism classes of all finite \(G\)-sets, which forms a semi-ring under the addition and multiplication induced respectively by the disjoint union and Cartesian product. The Grothendieck ring of \(S(G)\) is called the Burnside ring of \(G\), denoted by \(\Omega (G)\). Let \(\Omega (G)^*\) be the group of units of \(\Omega (G)\). The author of this paper investigates \(\Omega (G)^*\) for an elementary abelian 2-group \(G\), and gives a filtration \(\Omega (G)^*=\Omega_{-1} (G)^* \supset \Omega_0 (G)^* \supset \Omega_1(G)^* \supset\cdots\supset \Omega_n (G)^*\) when \(|G|= 2^n\).