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# Finite matrix group

Let be a finite subgroup of   this is the group of the invertible matrices over ). If then prove that .

Solution

Let us suppose that and . We note that for every the depiction such that is and onto. Thus:

Thus the matrix is idempotent. thus its trace equals to its class. (since we are over which is a field of zero characteristic.) Hence

This implies that hence .

The exercise can also be found at mathematica.gr

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