the sum of the values of a character of a finite group is
First assume that is trivial, i.e. for all we have . Then the result is clear.
Thus, let us assume that there exists in such that . Notice that for any element the map:
is clearly a bijection. Define . Then:
By the remark above, sums and are equal, since both run over all possible values of over elements of . Thus, we have proved that:
and . Since is a field, it follows that , as desired.
|Title||the sum of the values of a character of a finite group is|
|Date of creation||2013-03-22 14:10:30|
|Last modified on||2013-03-22 14:10:30|
|Last modified by||alozano (2414)|