Talk:Todd–Coxeter algorithm

what the H?
One implementation of the algorithm proceeds as follows. Suppose that $ G = \langle X \mid R \rangle $, where $ X $ is a set of generators and $ R $ is a set of relations and denote by $ X' $ the set of generators $ X $ and their inverses. Let $ H = \langle h_1, h_2, \ldots, h_s \rangle $ where the $ h_i $ are words of elements of $ X' $. There are three types of tables that will be used: a coset table, a relation table for each relation in $ R $, and a subgroup table for each generator $ h_i $ of $ H $. Information is gradually added to these tables, and once they are filled in, all cosets have been enumerated and the algorithm terminates. 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)
 * 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)