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 h_i from X′ whose images generate the subgroup H. This list and those words do not change during the course of the algorithm. JackSchmidt (talk)