Multiple Burnside rings and Brauer induction formulae

作者：Takegahara Yugen^*

来源：Journal of Algebra, 2010, 324(7): 1656-1686.

DOI：10.1016/j.jalgebra.2010.05.021

• Burnside ring
• Brauer's induction theorem

Let G be a finite group, and suppose that G is an operator group of a finite group A. Define S(G, A) = {(H, sigma) vertical bar H is an element of S(G) and sigma is an element of Z(1) (H, A)}, where S(G) is the set of subgroups of G and Z(1) (H, A) is the set of crossed homomorphisms from H to A. We view G as an operator group of the opposite group A degrees of A, and make S(G, A) into a left A degrees (sic)G-set. The ring Omega(G, A) is defined to be a commutative ring consisting of all formal Z-linear combinations of A degrees (sic) G-orbits in S(G, A). Idempotent formulae for Q circle times(Z) Omega(G, A) not only imply a generalization of Dress' induction theorem but bring, in the case where Z(1) (G, A) is the set of linear C-characters of G, Boltje's explicit formula for Brauer's induction theorem and its hyperelementary version.

• 出版日期2010-10-1