Some of the most beautiful mathematical objects found in the last
forty years are the sporadic simple groups. However, gaining
familiarity with these groups presents problems for two reasons.
First, they were discovered in many different ways, so to
understand their constructions in depth one needs to study lots of
different techniques. Second, since each of them is in a sense
recording some exceptional symmetry in spaces of certain
dimensions, they are by their nature highly complicated objects
with a rich underlying combinatorial structure. Motivated by
initial results which showed that the Mathieu groups can be
generated by highly symmetrical sets of elements, which themselves
have a natural geometric definition, the author develops from
scratch the notion of symmetric generation. He exploits this
technique by using it to define and construct many of the sporadic
simple groups including all the Janko groups and the Higman-Sims
group. This volume is suitable for researchers and postgraduates.
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