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Distance-Transitive Representations of the Sporadic Groups

Research output: Contribution to journalArticle

Author(s)

AA Ivanov, Stephen Alexander Linton, K Lux, J Saxl, LH Soicher

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Abstract

A permutation representation of a finite group is multiplicity-free if all the irreducible constituents in the permutation character are distinct. There are three main reasons why these representations are interesting: it has been checked that all finite simple groups have such permutation representations, these are often of geometric interest, and the actions on vertices of distance-transitive graphs are multiplicity-free.

In this paper we classify the primitive multiplicity-free representations of the sporadic simple groups and their automorphism groups. We determine all the distance-transitive graphs arising from these representations. Moreover, we obtain intersection matrices for most of these actions, which are of further interest and should be useful in future investigations of the sporadic simple groups.

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Details

Original languageEnglish
Pages (from-to)3379-3427
Number of pages49
JournalCommunications in Algebra
Volume23
Publication statusPublished - 1995

    Research areas

  • MAXIMAL-SUBGROUPS, LINEAR-GROUPS, BABY MONSTER, G LESS, GRAPHS, CONSTRUCTION

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