Quaternions over Q(√5), Leech's lattice and the sporadic group of Hall-Janko
نویسندگان
چکیده
منابع مشابه
Integral Group Ring of the First Janko Simple Group
We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Janko group J1. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.
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In this paper, we construct the Hall-Janko graph within the split Cayley hexagon H(4). Using this graph we then construct the near-octagon of order (2, 4) as a subgeometry of the dual of H(4), with J2 : 2 as its automorphism group. These constructions are based on a lemma determining the possibilities for the structure of the intersection of two subhexagons of order 2 in H(4).
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In two recent papers [Hafner, Elec. J. Combin. 11 (R77) (2004), 1–33; Ilić, Pace and Magliveras, J. Combin. Math. Combin. Comput. 80 (2012), 267–275] it was shown that the Higman-Sims graph Γ can be decomposed into a disjoint union of five double Petersen graphs. In the second of these papers, it was further shown that all such decompositions fall into a single orbit under the action of sporadi...
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In the present paper, we study the group SL 2 (H Z) of (2 2)-matrices with reduced norm 1 over the noncommutative ring of Hamilton quaternions with integral coeecients. In section 1, we obtain a presentation for SL 2 (H Z) in terms of generators and deening relations. In section 2, we exhibit a subgroup of nite index of SL 2 (H Z) with a nonabelian free quotient of rank 3. It is well known that...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90025-3