High Quality Content by WIKIPEDIA articles! Schreier's subgroup lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup. Suppose H is a subgroup of G, which is finitely generated with generating set S, that is, G = <S>. Let R be a right transversal of H in G. We make the definition that given g G, overline{g} is the chosen representative in the transversal R of the coset Hg, that is, gin Hoverline{g}. Then H is generated by the set {rs(overline{rs})^{-1}|rin R, sin S}.

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