Systematic Enumeration of Cosets
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 method into an almost mechanical technique, a useful tool with a wide range of applications. In § 2.1 we apply it to determine an abstract definition for a given finite group. In § 2.4 we use it to find whether a given subgroup of an abstract group is normal. Finally, in § 2.5 we see how it helps in determining properties of new abstract groups.
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