Algorithms for effectively computing with group homomorphisms are presented . Particular emphasis is given to those homomorphisms induced by invariant subsets and systems of imprimitivity of a permutation group, and by the right cosets of a subgroup in an arbitrarily represented group. The algorithms allow the computation of images and preimages of elements and subgroups, as well as the computation of the image and kernel of the homomorphism. A discussion of coset enumeration in permutation groups is included. © 1985, Academic Press Inc. (London) Ltd.. All rights reserved.
Butler, G. (1985). Effective computation with group homomorphisms. Journal of Symbolic Computation, 1(2), 143–157. https://doi.org/10.1016/S0747-7171(85)80011-0