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Minimally irreducible groups of prime degree

Published online by Cambridge University Press:  17 April 2009

F. Dalla Volta  and
L. Di Martino
F. Dalla Volta
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Bicocca degli Arcimboldi 8, I-20126 Milano, Italy e-mail: [email protected]@matapp.unimib.it
L. Di Martino
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Bicocca degli Arcimboldi 8, I-20126 Milano, Italy e-mail: [email protected]@matapp.unimib.it
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Abstract

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We determine the irreducible subgroups G of GL (r,ℂ), where r is prime and all proper subgroups of G are reducible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 335 - 345
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Brauer, R., ‘Über endliche lineare Gruppen von Primzahlgrad’, Math. Ann. 169 (1967), 73–96.CrossRefGoogle Scholar
[2]Dornhoff, L., Group representation theory, Part A (M. Dekker Inc., New York, 1971).Google Scholar
[3]Dixon, J.D. and Zalesskii, A.E., ‘Finite primitive linear groups of prime degree’, J. London Math. Soc. (2) 57 (1998), 126–134.CrossRefGoogle Scholar
[4]Dixon, J.D. and Zalesskii, A.E., ‘Monomial complex finite irreducible linear groups of prime degree’, (in preparation).Google Scholar
[5]Gérardin, P., ‘Weil representations associated to finite fields’, J. Algebra 46 (1977), 54–101.CrossRefGoogle Scholar
[6]Howe, R.E., ‘On the character of Weil's representation’, Trans. Amer. Math. Soc. 177 (1973), 287–298.Google Scholar
[7]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[8]Kleidman, P. and Liebeck, M., The subgroup structure of the finite classical groups, London Math. Soc. Lecture Notes 129 (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
[9]Landazuri, V. and Seitz, G.M., ‘On the minimal degree of projective representations of the finite Chevalley groups’, J. Algebra 32 (1974), 418–443.CrossRefGoogle Scholar
[10]Platonov, V.P., ‘Finiteness of minimal irreducible linear groups’, (Russian), Vesc. Acad. Navuk BSSR Ser. Fiz-Mat. Navuk 5 (1975), 96–97.Google Scholar
[11]Rédei, L., ‘Das “schiefe Produkt” in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehören’, Comment Math. Helv. 20 (1947), 225–264.CrossRefGoogle Scholar
[12]Seitz, G.M., ‘Some representations of classical groups’, J. London Math. Soc. (2) 10 (1975), 115–120.CrossRefGoogle Scholar
[13]Suprunenko, D.A., Matrix groups, Transl. Math. Monographs, (translated from the 1972 Russian edition) (Amererican Math. Society, Providence, 1976).CrossRefGoogle Scholar
[14]Suprunenko, D.A., ‘Minimal irreducible solvable linear groups of prime degree’, Soviet Math. Dokl. 13 (1972), 979–981.Google Scholar
[15]Suprunenko, D.A., ‘Minimal irreducible solvable linear groups of prime degree’, (in Russian), Trudy Moskov. Mat. Obshch. 29 (1973), 223–234.Google Scholar
[16]Tiep, Pham Huu and Zalesskii, A.E., ‘Some characterizations of the Weil representations of the symplectic and unitary groups’, J. Algebra 192 (1997), 130–165.CrossRefGoogle Scholar
[17]Ward, H.N., ‘Representations of symplectic groups’, J. Algebra 20 (1972), 182–195.CrossRefGoogle Scholar
[18]Zalesskii, A.E. and Suprunenko, I.D., ‘Permutation representations and a fragment of the decomposition matrix of symplectic and linear groups over a finite field’, Siberian Mat. J. 31 (1990), 744–755.CrossRefGoogle Scholar