When we began to consider the scope of this book we envisaged a catalogue supplying at least
one abstract definition for any finitely generated group that the reader might propose. But we
soon realized that more or less arbitrary restrictions are necessary because interesting
groups are so numerous. For permutation groups of degree 8 or less (i.e.' .subgroups of es)
the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915) while keeping an
eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order finite
and infinite groups of congruent transformations symmetric and alternating groups linear
fractional groups and groups generated by reflections in real Euclidean space of any number of
dimensions. The best substitute for a more extensive catalogue is the description (in Chapter
2) of a method whereby the reader can easily work out his own abstract definition for almost
any given finite group. This method is sufficiently mechanical for the use of an electronic
computer.
