the characteristic embedding of the Burnside ring
Denote by the cardinality of a set .
It is easy to see that for any -sets we have:
Denote by . Recall that any are said to be conjugate iff there exists such that . Conjugation is an equivalence relation. Denote by the quotient set.
One can check that for any such that is conjugate to and for any finite -set we have
Thus we have a well defined ring homomorphism:
|Title||the characteristic embedding of the Burnside ring|
|Date of creation||2013-03-22 18:08:09|
|Last modified on||2013-03-22 18:08:09|
|Last modified by||joking (16130)|