On the generalized burnside ring with respect to the young subgroups of the symmetric group

We determine the number of blocks of the generalized Burnside ring of the s ymmetric group S-n with respect to the Young subgroups of S-n over a field of characteristic p. Let kS(n) be a group algebra of S-n over a field k of characteristic p > 0 and R(kS(n))((p)) the Grothendieck ring of kS(n) over p-local integers. Then, as a corollary of the theorem, we have that F x R(k S(n))((p)) is semisimple, where F is any field of characteristic p. It is w ell known that the result holds for an arbitrary finite group, but our appr oach to the result is remarkable. (C) 2001 Academic Press.