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It is often the case that a particular expression in the original
generators is important in some homomorphic image of the group
in the sense that it will very often form a common subexpression
of subsequent expression. For this reason,
Magma provides facilities to build related SLP-groups
in which particular words acquire generator status themselves.
An SLP-group H on n + q generators (where G has n generators
and Q has q elements). Furthermore, the identification of
G.i with H.i (i≤n) and of Q[i] with H.(n + i) is maintained,
allowing coercion between G and H and also simple definition of
homomorphisms.
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