proof of Nielsen-Schreier theorem and Schreier index formula
While there are purely algebraic proofs of the Nielsen-Schreier theorem, a much easier proof is available through geometric group theory.
Moreover, we can obtain the rank of (the size of the set on which it is free). If is a finite graph, then is free of rank , where denotes the Euler characteristic of . Since , the rank of is . If is of finite index in , then is finite, and . Of course is the rank of . Substituting, we obtain the Schreier index formula:
|Title||proof of Nielsen-Schreier theorem and Schreier index formula|
|Date of creation||2013-03-22 13:56:02|
|Last modified on||2013-03-22 13:56:02|
|Last modified by||mathcam (2727)|