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One implementation of the algorithm proceeds as follows. Suppose that , where is a set of generators and is a set of relations and denote by the set of generators and their inverses. Let where the are words of elements of . There are three types of tables that will be used: a coset table, a relation table for each relation in , and a subgroup table for each generator of . Information is gradually added to these tables, and once they are filled in, all cosets have been enumerated and the algorithm terminates.
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I'm lost already. Is H a list of words or a list of generators? Does it begin empty, or what? —Tamfang (talk) 06:13, 2 September 2012 (UTC)[reply]
H is a subgroup of G, and does not change during the course of the algorithm. H is represented by a list of words hi from X′ whose images generate the subgroup H. This list and those words do not change during the course of the algorithm. JackSchmidt (talk)