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Modular permutation representations. (English) Zbl 0285.20012

MSC:
20C20 Modular representations and characters
16S34 Group rings
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
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[1] A. Adrian Albert, Structure of algebras, Revised printing. American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961.
[2] Emil Artin, Cecil J. Nesbitt, and Robert M. Thrall, Rings with Minimum Condition, University of Michigan Publications in Mathematics, no. 1, University of Michigan Press, Ann Arbor, Mich., 1944. · Zbl 0060.07701
[3] Richard Brauer, Zur Darstellungstheorie der Gruppen endlicher Ordnung. II, Math. Z. 72 (1959/1960), 25 – 46 (German). · doi:10.1007/BF01162934 · doi.org
[4] 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. · Zbl 0131.25601
[5] Walter Feit, Some properties of the Green correspondence, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp. 139 – 148.
[6] Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. · Zbl 0228.20019
[7] J. A. Green, Blocks of modular representations, Math. Z. 79 (1962), 100 – 115. · Zbl 0233.20006 · doi:10.1007/BF01193108 · doi.org
[8] J. A. Green, A transfer theorem for modular representations, J. Algebra 1 (1964), 73 – 84. · Zbl 0126.05502 · doi:10.1016/0021-8693(64)90009-2 · doi.org
[9] James A. Green, Some remarks on defect groups, Math. Z. 107 (1968), 133 – 150. · Zbl 0164.34002 · doi:10.1007/BF01111026 · doi.org
[10] D. G. Higman, Modules with a group of operators, Duke Math. J. 21 (1954), 369 – 376. · Zbl 0055.25502
[11] D. G. Higman, Intersection matrices for finite permutation groups, J. Algebra 6 (1967), 22 – 42. · Zbl 0183.02704 · doi:10.1016/0021-8693(67)90011-7 · doi.org
[12] Gordon Keller, Concerning the degrees of irreducible characters, Math. Z. 107 (1968), 221 – 224. · Zbl 0186.32801 · doi:10.1007/BF01110260 · doi.org
[13] L. L. Scott, Uniprimitive groups of degree \( kp\), Ph. D. Thesis, Yale University, New Haven, Conn., 1968.
[14] -, Uniprimitive permutation groups, Theory of Finite Groups, (Sympos., Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969), pp. 55-62.
[15] L. Scott, The modular theory of permutation representations, Representation theory of finite groups and related topics (Proc. Sympos. Pure Math., Vol. XXI, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 137 – 144.
[16] O. Tamaschke, A generalized character theory on finite groups, Proc. Internat. Conf. Theory of Groups, Austral. Nat. U. Canberra, August 1965, New York, 1967, pp. 347-355.
[17] Edwin Weiss, Algebraic number theory, McGraw-Hill Book Co., Inc., New York-San Francisco-Toronto-London, 1963. · Zbl 0115.03601
[18] Helmut Wielandt, Finite permutation groups, Translated from the German by R. Bercov, Academic Press, New York-London, 1964. · Zbl 0138.02501
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