Suppose that is a group acting (http://planetmath.org/GroupAction) on a set . For each , let be the orbit of , let be the stabilizer of , and let be the set of left cosets of . Then for each the function defined by is a bijection. In particular,
for all .
If is such that for some , then we have , and so , and therefore . This shows that is well-defined.
|Date of creation||2013-03-22 12:23:10|
|Last modified on||2013-03-22 12:23:10|
|Last modified by||yark (2760)|