Experimental Mathematics

The primitive distance-transitive representations of the Fischer groups

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

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.

Article information

Source
Experiment. Math., Volume 4, Issue 3 (1995), 235-253.

Dates
First available in Project Euclid: 3 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1062621081

Mathematical Reviews number (MathSciNet)
MR1387480

Zentralblatt MATH identifier
0855.20014

Subjects
Primary: 20C34: Representations of sporadic groups
Secondary: 20D08: Simple groups: sporadic groups

Citation

Linton, Stephen A.; Lux, Klaus; Soicher, Leonard H. The primitive distance-transitive representations of the Fischer groups. Experiment. Math. 4 (1995), no. 3, 235--253. https://projecteuclid.org/euclid.em/1062621081


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