Schreier's Subgroup Lemma
978-613-1-15690-8
6131156905
108
2010-08-10
39.00 €
eng
https://images.our-assets.com/cover/230x230/9786131156908.jpg
https://images.our-assets.com/fullcover/230x230/9786131156908.jpg
https://images.our-assets.com/cover/2000x/9786131156908.jpg
https://images.our-assets.com/fullcover/2000x/9786131156908.jpg
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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}. Let us establish the evident fact that the group Z3=Z/3Z is indeed cyclic. Via Cayley's theorem, Z3 is a subgroup of the symmetric group S3. Now, Bbb{Z}_3={ e, (1 2 3), (1 3 2) } S_3={ e, (1 2), (1 3), (2 3), (1 2 3), (1 3 2) } where e is the identity permutation. Note S3 = < { s1=(1 2), s2=(1 2 3) } >.
https://www.morebooks.de/books/gb/published_by/betascript-publishing/1/products
Mathematics
https://www.morebooks.de/store/gb/book/schreier-s-subgroup-lemma/isbn/978-613-1-15690-8