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Subgroups of N.E.C. groups and finite permutation groups. (English) Zbl 0693.20044
The author shows how to obtain the signature of a subgroup of a non- euclidean crystallographic group (NEC-group) from the action of the generators of the group on the cosets. The method developed is a purely mechanical process which can be carried out on a computer. The results of this paper generalize those which had been obtained by the reviewer and other authors on normal subgroups of NEC groups so as the results of D. Singerman [Bull. Lond. Math. Soc. 2, 319-323 (1970; Zbl 0206.308)] on subgroups of Fuchsian groups. Recently Frennessy and S. J. Pride have obtained the same result [J. Algebra 120, 200-223 (1989; Zbl 0679.20033)] by using N.E.C. complexes and covering spaces.
Reviewer: E.Bujalance

MSC:
20H15 Other geometric groups, including crystallographic groups
20E07 Subgroup theorems; subgroup growth
20-04 Software, source code, etc. for problems pertaining to group theory
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