The geometry of the Hall-Janko group as a quaternionic reflection group

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1986 English Publisher:Springer Science and Business Media LLCJournal:Geometriae Dedicata, volume 20, pages 157-173 (issn: 0046-5755, eissn: 1572-9168,

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Authors: Wilson, Robert A.;

doi: 10.1007/bf00164397

The geometry of the Hall-Janko group as a quaternionic reflection group

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Abstract

The author describes how the Hall-Janko group \(J_ 2\), or rather, its double cover \(2J_ 2\), can be identified with the symmetry group of the icosian Leech lattice L. He gives an interesting correspondence between the maximal subgroups of \(2J_ 2\) and certain geometric figures connected to L.

Related Organizations

University of Cambridge
United Kingdom

Keywords

Leech lattice, Reflection groups, reflection geometries, Hall-Janko group, Series and lattices of subgroups, Simple groups: sporadic groups, quaternionic reflection group

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