Schreier index formula

Let F be a free groupMathworldPlanetmath of finite rank, and let H be a subgroupMathworldPlanetmathPlanetmath ( of finite index in F. By the Nielsen-Schreier theorem, H is free. The Schreier index formula states that


This implies more generally that if G is a group generated by m elements, then any subgroup of index n in G can be generated by at most nm-n+1 elements.

Title Schreier index formula
Canonical name SchreierIndexFormula
Date of creation 2013-03-22 13:56:18
Last modified on 2013-03-22 13:56:18
Owner yark (2760)
Last modified by yark (2760)
Numerical id 14
Author yark (2760)
Entry type Theorem
Classification msc 20E05
Related topic ProofOfNielsenSchreierTheoremAndSchreierIndexFormula