Concept

Schreier's lemma

Summary
In mathematics, Schreier's lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup. Statement Suppose H is a subgroup of G, which is finitely generated with generating set S, that is, G = \langle S\rangle. Let R be a right transversal of H in G. In other words, R is (the image of) a section of the quotient map G \to H\backslash G, where H\backslash G denotes the set of right cosets 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, :g\in H\overline{g}. Then H is generated by the set :{rs(\overline{rs})^{-1}|r\in R, s\in S}. Hence, in particular, Schreier'
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