A correlation between $\textrm {PSU}_{4} (3)$, the Suzuki group, and the Conway group
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- by J. H. Lindsey PDF
- Trans. Amer. Math. Soc. 157 (1971), 189-204 Request permission
Abstract:
We shall use a six dimensional projective representation of $PS{U_4}(3)$ of order ${2^7}{3^6}5 \cdot 7$ to construct 12 and $24$-dimensional complex projective representations of the Suzuki and Conway groups, respectively, acting on the Leech lattice. The construction makes it easy to show that the Suzuki and Conway simple groups have outer automorphism groups of order two and one, respectively. Also, the simple Suzuki group contains $3 \cdot PS{U_4}(3) \cdot 2,{3^5} \cdot {M_{11}}$, and a group which is probably $PS{U_5}(2)$, where $A \cdot B$ denotes an extension of the group $A$ by the group $B$.References
- J. H. Conway, A group of order $8,315,553,613,086,720,000$, Bull. London Math. Soc. 1 (1969), 79β88. MR 248216, DOI 10.1112/blms/1.1.79
- Richard Brauer, Γber endliche lineare Gruppen von Primzahlgrad, Math. Ann. 169 (1967), 73β96 (German). MR 206088, DOI 10.1007/BF01399532 J. H. Lindsey II, Linear groups with an irreducible, normal, rank two $p$-subgroup (to appear). β, Finite linear groups of degree six (to appear). β, On a six-dimensional projective representation of $PS{U_4}(3)$, Pacific J. Math. 36 (1971).
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 189-204
- MSC: Primary 20.75
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283097-8
- MathSciNet review: 0283097