On maximal finite irreducible subgroups of 𝐺𝐿(𝑛,𝑍). II. The six dimensional case

Plesken, Wilhelm; Pohst, Michael

doi:10.1090/S0025-5718-1977-0444790-6

On maximal finite irreducible subgroups of $\textrm {GL}(n, \textbf {Z})$. II. The six dimensional case

Authors: Wilhelm Plesken and Michael Pohst
Journal: Math. Comp. 31 (1977), 552-573
MSC: Primary 20G05
DOI: https://doi.org/10.1090/S0025-5718-1977-0444790-6
MathSciNet review: 0444790
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: All maximal finite absolutely irreducible subgroups of $GL(6,{\mathbf {Z}})$ are determined up to Z-equivalence.

H. F. BLICHFELDT, Finite Collineation Groups, Univ. of Chicago Press, Chicago, 1917.

E. C. Dade, Integral systems of imprimitivity, Math. Ann. 154 (1964), 383–386. MR 161919, DOI https://doi.org/10.1007/BF01362571
Veikko Ennola, On the characters of the finite unitary groups, Ann. Acad. Sci. Fenn. Ser. A I No. 323 (1963), 35. MR 0156900
James E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. MR 0323842
J. H. Lindsey II, Finite linear groups of degree six, Canadian J. Math. 23 (1971), 771–790. MR 289665, DOI https://doi.org/10.4153/CJM-1971-086-x

H. MINKOWSKI, "Zur Theorie der positiven quadratischen Formen," Gesammelte Werke, Band 1, Chelsea, New York, 1958, pp. 212-218.

Wilhelm Plesken and Michael Pohst, On maximal finite irreducible subgroups of ${\rm GL}(n, {\bf Z})$. I. The five and seven dimensional cases, Math. Comp. 31 (1977), no. 138, 536–551. MR 444789, DOI https://doi.org/10.1090/S0025-5718-1977-0444789-X

W. PLESKEN, Beiträge zur Bestimmung der endlichen irreduziblen Untergruppen von $GL(n,{\mathbf {Z}})$ und ihrer ganzzahligen Darstellungen, Dissertation, Aachen, 1974.

I. SCHUR, "Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen," Gesammelte Abhandlungen, Band 1, Springer-Verlag, Berlin and New York, 1973, pp. 198-250.

I. SCHUR, "Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen," Gesammelte Abhandlungen, Band 1, Springer-Verlag, Berlin and New York, 1973, pp. 346-441.

Olga Taussky, On a theorem of Latimer and MacDuffee, Canad. J. Math. 1 (1949), 300–302. MR 30491, DOI https://doi.org/10.4153/cjm-1949-026-1