Abstract
E. H. Moore (1897) and many others have computed the index of a subgroup in an abstract group by systematically enumerating the cosets. Todd and Coxeter (1936) converted this into a mechanical technique, a useful tool with a wide range of applications. In § 2.1 we describe this algorithm, in § 2.2 we use it to determine an abstract definition for a given finite group, and in § 2.3 we describe some additional computation, performed alongside the enumeration, which determines an abstract definition for the subgroup.
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© 1980 Springer-Verlag Berlin Heidelberg
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Coxeter, H.S.M., Moser, W.O.J. (1980). Systematic Enumeration of Cosets. 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_2
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DOI: https://doi.org/10.1007/978-3-662-21943-0_2
Publisher Name: Springer, Berlin, Heidelberg
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