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Note on a theorem of Schreier

1957; American Mathematical Society; Volume: 8; Issue: 4 Linguagem: Inglês

10.1090/s0002-9939-1957-0086813-1

1088-6826

A. Karrass, D. Solitar,

Mathematical and Theoretical Analysis

Schreier [2] showed (using graph techniques) that if F is a free group and H is a normal subgroup which is finitely generated, then H must be of finite index in F. We give an algebraic proof of the following generalization: Theorem 1.Let F be a free group on the free generators {a,} and let H be a finitely generated subgroup containing a normal subgroup of F.