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. A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... Group theory is that branch of mathematics concerned with the study of groups. ... The Schreier-Sims algorithm is an efficient method of computing a strong generating set (SGS) of a permutation group. ... In mathematics, one method of defining a group is by a presentation. ... In mathematics, given a group G under a binary operation *, we say that some subset H of G is a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H is a group operation...

Let S be a set of generators for a group G. Let H be a subgroup of G with a right transversal R, such that In abstract algebra, a generating set of a group is a subset S such that every element of G can be expressed as the product of finitely many elements of S and their inverses. ... Given a collection C of disjoint sets, a transversal is a set containing exactly one member of each of them. ...

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For , define to be the unique element in

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Then H is generated by the set SET may refer to: Secure electronic transaction, a protocol used for credit card processing, Simulated Emergency Test, an Amateur radio training exercise, Society for the Eradication of Television, Stock Exchange of Thailand, a national stock exchange of Thailand, SET Index, an index for Stock Exchange of Thailand This is a...

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References

• Seress, A. Permutation Group Algorithms. Cambridge University Press, 2002.