Geodesic
Automorphism groups of some Mordell--Weil lattices
Izvestiya. Mathematics , Tome 40 (1993) no. 3, pp. 477-501.

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The automorphism groups $G=\operatorname{Aut}(\Lambda)$ are calculated for the Mordell–Weil lattices connected with globally irreducible representations of the simple groups $S=\operatorname{PSL}(2,p)$ ($p$ a prime, $p\equiv 3$ $(\operatorname{mod}4)$) and $S=\operatorname{PSU}(3,q)$ $(q=p^f>2)$ of degree $p-1$ and $2q(q-1)$, respectively. In particular, it is shown that in the great majority of cases $S$ is the unique nonabelian composition factor of $G$. 
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     title = {Automorphism groups of some {Mordell--Weil} lattices},
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Pham Huu Tiep. Automorphism groups of some Mordell--Weil lattices. Izvestiya. Mathematics , Tome 40 (1993) no. 3, pp. 477-501. http://geodesic.mathdoc.fr/item/IM2_1993_40_3_a1/

[1] Elklies N., Letters to N. J. A. Sloane, Aug. 15, 1989; Sept. 15, 1989

[2] Gross B. H., “Group representations and lattices”, J. Amer. Math. Soc., 3 (1990), 929–960 | DOI | MR | Zbl

[3] Thompson J. G., “Finite groups and even lattices”, J. Algebra, 38:2 (1976), 523–524 | DOI | MR | Zbl

[4] Conway J. H., “A characterisation of Leech's lattice”, Invent. Math., 7 (1969), 137–14 | DOI | MR

[5] Thompson J. G., “A simple subgroup of $E_8(3)$”, Finite Groups, Symposium N. Iwahri Japan Soc. for Promotion of Science, 1976, 113–116

[6] Gow R., “Unimodular integral lattices associated with the basic spin representations of $2A_n$ and $2S_n$”, Bull. London Math. Soc., 21 (1989), 257–262 | DOI | MR | Zbl

[7] Pirs P., Assotsiativnye algebry, Mir, M., 1986 | MR

[8] Conway J. I., Sloane N. J. A., Sphere packings, lattices and groups, 290, Springer, Grundlehren, 1988 | MR | Zbl

[9] Conway J. H. et al., ATLAS of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[10] McKay J. H., “The non-abelian simple groups $G$, $|G|10^6$ – character tables”, Comm. Algebra, 7:13 (1979), 1407–1445 | DOI | MR | Zbl

[11] Adler A., “Some integral representations of $PSL(2,p)$ and their applications”, J. Algebra, 72 (1981), 115–145 | DOI | MR | Zbl

[12] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1972 | MR

[13] Bondal A. I., “Invariantnye reshetki tipa $A_{p-1}$”, Vest. MGU. Ser. 1. Matematika. Mekhanika, 1986, no. 1, 52–54 | MR | Zbl

[14] Fam Khyu Ten, “Invariantnye podreshetki v odnoi kartanovskoi podalgebre”, Vest. MGU. Ser. 1. Matematika. Mekhanika, 1988, no. 4, 72–75 | Zbl

[15] Feit W., “Groups with a cyclic Sylow subgroup”, Nagoya Math. J., 27:2 (1966), 571–584 | MR | Zbl

[16] Hall P., Higman G., “On the $p$-length of $p$-soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc., 6:21 (1956), 1–42 | DOI | MR | Zbl

[17] Kertis Ch., Reiner I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[18] “Cooperstein B. N.”, Israel J. Math., 30 (1978), 213–235 | DOI | MR | Zbl

[19] Landazuri V., Seitz G. M., “On the minimal degrees of projective representations of the finite Chevalley groups”, J. Algebra, 32 (1974), 418–443 | DOI | MR | Zbl

[20] Carter R., Finite groups of Lie type, John Wiley, 1985 | MR | Zbl

[21] Amitsur S. A., “Finite subgroups of division rings”, Trans. Amer. Math. Soc., 80:2 (1955), 361–386 | DOI | MR | Zbl

[22] Zsigmondy K., “Zur theorie der Potenzreste”, Monath. Math. Phys., 3 (1892), 265–284 | DOI | MR

[23] Rasala R., “On the minimal degrees of characters of $\mathfrak{S}$”, J. Algebra, 45:1 (1977), 132–181 | DOI | MR | Zbl

[24] Wagner A., “An observation on the degrees of projective representations of the symmetric and alternating groups over an arbitrary field”, Arch. Math., 29 (1977), 583–589 | DOI | MR | Zbl

[25] Liebeck M. W., “On the orders of maximal subgroups of the finite classical groups”, Proc. London. Math. Soc. (3), 50 (1985), 426–446 | DOI | MR | Zbl

[26] Conway J. H., Sloane N. J. A, “The Coxeter lattice, the Mitchell group and related sphere packings”, Math. Proc. Camb. Phil. Soc., 93:3 (1983), 421–440 | DOI | MR | Zbl

[27] Feit W., “Some lattices over $\mathbf{Q}(\sqrt{-3})$”, J. Algebra, 52 (1978), 248–263 | DOI | MR | Zbl

[28] Wilson R. A., “The quaternionic lattice for $2G_2(4)$ and its maximal subgroups”, J. Algebra, 77 (1982), 449–466 | DOI | MR | Zbl

[29] Lindsey J. H., “A new lattice for the Hall–Janko group”, Proc. Amer. Math. Soc., 103:3 (1988), 703–709 | DOI | MR | Zbl