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On maximal finite irreducible subgroups of . I. The five and seven dimensional cases
Authors:
Wilhelm Plesken and Michael Pohst
Journal:
Math. Comp. 31 (1977), 536-551
MSC:
Primary 20G05
MathSciNet review:
0444789
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Abstract: General methods for the determination of maximal finite absolutely irreducible subgroups of are described. For all these groups are computed up to Z-equivalence.
- [1]
R. BÜLOW, Über Dadegruppen in
, Dissertation, Aachen, 1973.
- [2]
R. BÜLOW, J. NEUBÜSER & H. WONDRATSCHEK, "On crystallography in higher dimensions. I, II, III," Acta Cryst., v. A27, 1971, pp. 517-535.
- [3]
Richard
Brauer, Über endliche lineare Gruppen von Primzahlgrad,
Math. Ann. 169 (1967), 73–96 (German). MR 0206088
(34 #5913)
- [4]
R.
Brauer and C.
Nesbitt, On the modular characters of groups, Ann. of Math.
(2) 42 (1941), 556–590. MR 0004042
(2,309c)
- [5]
Charles
W. Curtis and Irving
Reiner, Representation theory of finite groups and associative
algebras, Pure and Applied Mathematics, Vol. XI, Interscience
Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979
(26 #2519)
- [6]
E.
C. Dade, The maximal finite groups of 4×4 integral
matrices, Illinois J. Math. 9 (1965), 99–122.
MR
0170958 (30 #1192)
- [7]
Veikko
Ennola, On the characters of the finite unitary groups, Ann.
Acad. Sci. Fenn. Ser. A I No. 323 (1963), 35. MR 0156900
(28 #143)
- [8]
James
E. Humphreys, Introduction to Lie algebras and representation
theory, Springer-Verlag, New York, 1972. Graduate Texts in
Mathematics, Vol. 9. MR 0323842
(48 #2197)
- [9]
H. MINKOWSKI, "Zur Theorie der positiven quadratischen Formen," Gesammelte Werke, Band 1, Chelsea, New York, 1958, pp. 212-218.
- [10]
W. PLESKEN, Beiträge zur Bestimmung der endlichen irreduziblen Untergruppen von
und ihrer ganzzahligen Darstellungen, Dissertation, Aachen, 1974.
- [11]
S.
S. Ryškov, The maximal finite groups of integer
𝑛×𝑛 matrices, Dokl. Akad. Nauk SSSR
204 (1972), 561–564 (Russian). MR 0304501
(46 #3636)
- [12]
S.
S. Ryškov, Maximal finite groups of
𝑛×𝑛 integral matrices and full integral automorphism
groups of positive quadratic forms (Bravais types), Trudy Mat. Inst.
Steklov. 128 (1972), 183–211, 261 (Russian).
Collection of articles dedicated to Academician Ivan Matveevič
Vinogradov on his eightieth birthday, II. MR 0344199
(49 #8939)
- [13]
David
B. Wales, Finite linear groups in seven
variables, Bull. Amer. Math. Soc. 74 (1968), 197–198. MR 0218466
(36 #1552), http://dx.doi.org/10.1090/S0002-9904-1968-11939-1
- [14]
H. ZASSENHAUS, "Neuer Beweis der Endlichkeit der Klassenzahl bei unimodularer Äquivalenz endlicher ganzzahliger Substitutionsgruppen," Abh. Math. Sem. Univ. Hamburg, v. 12, 1938, pp. 276-288.
- [1]
- R. BÜLOW, Über Dadegruppen in
, Dissertation, Aachen, 1973.
- [2]
- R. BÜLOW, J. NEUBÜSER & H. WONDRATSCHEK, "On crystallography in higher dimensions. I, II, III," Acta Cryst., v. A27, 1971, pp. 517-535.
- [3]
- R. BRAUER, "Über endliche lineare Gruppen von Primzahlgrad," Math. Ann., v. 169, 1967, pp. 73-96. MR 34 #5913. MR 0206088 (34:5913)
- [4]
- R. BRAUER & C. NESBITT, "On modular characters of groups," Ann. of Math. (2), v. 42, 1941, pp. 556-590. MR 2, 309. MR 0004042 (2:309c)
- [5]
- W. C. CURTIS & I. REINER, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York and London, 1962. MR 26 #2519. MR 0144979 (26:2519)
- [6]
- E. C. DADE, "The maximal finite groups of
integral matrices," Illinois J. Math., v. 9, 1965, pp. 99-122. MR 30 #1192. MR 0170958 (30:1192)
- [7]
- V. ENNOLA, "On the characters of the finite unitary groups," Ann. Acad. Sci. Fenn. Ser. AI, No, 323, Helsinki, 1963. MR 28 #143. MR 0156900 (28:143)
- [8]
- J. E. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Math., vol. 9, Springer-Verlag, Berlin and New York, 1972. MR 48 #2197. MR 0323842 (48:2197)
- [9]
- H. MINKOWSKI, "Zur Theorie der positiven quadratischen Formen," Gesammelte Werke, Band 1, Chelsea, New York, 1958, pp. 212-218.
- [10]
- W. PLESKEN, Beiträge zur Bestimmung der endlichen irreduziblen Untergruppen von
und ihrer ganzzahligen Darstellungen, Dissertation, Aachen, 1974.
- [11]
- S. S. RYšSKOV, "On maximal finite groups of integer
-matrices," Dokl. Akad. Nauk SSSR, v. 204, 1972, pp. 561-564 = Soviet Math. Dokl., v. 13, 1972, pp. 720-724. MR 46 #3636. MR 0304501 (46:3636)
- [12]
- S. S. RYŠKOV, "Maximal finite groups of integral
matrices and full groups of integral automorphisms of positive quadratic forms (Bravais models)," Trudy Mat. Inst. Steklov., v. 128, 1972, pp. 183-211, 261 = Proc. Steklov Inst. Math., v. 128, 1972, pp. 217-250. MR 49 #8939. MR 0344199 (49:8939)
- [13]
- D. B. WALES, "Finite linear groups in seven variables," Bull. Amer. Math. Soc., v. 74, 1968, pp. 197-198. MR 36 #1552. MR 0218466 (36:1552)
- [14]
- H. ZASSENHAUS, "Neuer Beweis der Endlichkeit der Klassenzahl bei unimodularer Äquivalenz endlicher ganzzahliger Substitutionsgruppen," Abh. Math. Sem. Univ. Hamburg, v. 12, 1938, pp. 276-288.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1977-0444789-X
PII:
S 0025-5718(1977)0444789-X
Keywords:
Integral matrix groups
Article copyright:
© Copyright 1977 American Mathematical Society
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