Abstract
The importance of the symmetric group is obvious from the fact that any finite group, of order n, say, is a subgroup of S n . The procedure for obtaining generators and relations for S n can be carried over almost unchanged for a certain infinite group, first studied by Artin (1926); accordingly, we begin by describing this so-called braid group. The symmetric group (§ 6.2) has a subgroup A n , of index 2 (§ 6.3), which is particularly interesting because, when n > 4, it is simple.
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© 1980 Springer-Verlag Berlin Heidelberg
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Coxeter, H.S.M., Moser, W.O.J. (1980). The Symmetric, Alternating, and other Special Groups. In: Generators and Relations for Discrete Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21943-0_6
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DOI: https://doi.org/10.1007/978-3-662-21943-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-21945-4
Online ISBN: 978-3-662-21943-0
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