A new lattice for the Hall-Janko group
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- by J. H. Lindsey PDF
- Proc. Amer. Math. Soc. 103 (1988), 703-709 Request permission
Abstract:
Six by six matrix generators with entries in the rational numbers adjoined by a fifth root of unity, and most of these entries 0, are given for the proper central extension of the cyclic group of order 2 by the Hall-Janko group. They are found to preserve a $24$-dimensional lattice giving a packing of unit spheres with density about one fourth that of the Leach lattice.References
- J. H. Lindsey II, On a six dimensional projective representation of the Hall-Janko oroup, Pacific J. Math. 35 (1970), 175–186. MR 272888, DOI 10.2140/pjm.1970.35.175
- J. H. Lindsey II, Finite linear groups of degree six, Canadian J. Math. 23 (1971), 771–790. MR 289665, DOI 10.4153/CJM-1971-086-x
- J. Tits, Quaternions over $\textbf {Q}(\sqrt {5})$, Leech’s lattice and the sporadic group of Hall-Janko, J. Algebra 63 (1980), no. 1, 56–75. MR 568564, DOI 10.1016/0021-8693(80)90025-3
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 703-709
- MSC: Primary 20G20; Secondary 11H06, 20D08, 20G05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947642-7
- MathSciNet review: 947642