The primitive distance-transitive representations of the Fischer groups

Stephen A. Linton, Klaus Lux, Leonard H. Soicher

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Abstract

We classify the primitive distance-transitive representations of the Fischer sporadic simple groups and their automorphism groups. It turns out that the only primitive distance-transitive representations of these groups are their rank 3 representations. In the process of our work, we also classify and study the primitive multiplicity-free permutation representations of these Fischer groups. Our methods, which we describe in some detail, demonstrate the use of computational and randomized techniques in the classification of distance-transitive graphs and the study of very large permutation representations.

Original languageEnglish (US)
Pages (from-to)235-253
Number of pages19
JournalExperimental Mathematics
Volume4
Issue number3
DOIs
StatePublished - Jan 1 1995
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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