F. Oda et T. Yoshida, On the generalized burnside ring with respect to the young subgroups of the symmetric group, J ALGEBRA, 236(1), 2001, pp. 349-354
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.