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A new lattice for the Hall-Janko group


Author: J. H. Lindsey
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
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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 [Enhancements On Off] (What's this?)

  • [1] J. H. Lindsey II, On a six dimensional projective representation of the Hall-Janko group, Pacific J. Math. 35 (1970), 175-186. MR 0272888 (42:7769)
  • [2] -, Finite linear groups of degree six, Canad. J. Math. 23 (1971), 771-790. MR 0289665 (44:6853)
  • [3] J. Tits, Quaternions over $ Q({5^{1/2}})$, Leech's lattice and the sporadic group of Hall-Janko, J. Algebra 63 (1980), 56-75. MR 568564 (82k:20034)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0947642-7
Article copyright: © Copyright 1988 American Mathematical Society

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