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Block Idempotents and Normal p-Subgroups

Published online by Cambridge University Press:  22 January 2016

W. F. Reynolds*
Affiliation:
Tufts University
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In the theory of modular representations of a finite group G in an algebraically closed field Ω of characteristic p, Brauer has proved a useful reduction theorem for blocks [2, §§11, 12], [5, (88.8)], which can be reformulated as follows:

THEOREM 1 (Brauer). Let P bean arbitraryp-subgroup of G; let N = NG(P) and W = PCG(P).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Artin, E., Nesbitt, C., and Thrall, R., Rings with minimum condition, University of Michigan Press, Ann Arbor, 1948.Google Scholar
[2] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung I, Math. Z., 63 (1956), 406444.Google Scholar
[3] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung II, Math. Z., 72 (1959), 2546.Google Scholar
[4] Conlon, S. B., Twisted group algebras and their representations, J. Austral. Math. Soc., 4 (1964), 152173.Google Scholar
[5] Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience, New York, 1962.Google Scholar
[6] Fong, P., On the characters of p-solvable groups, Trans. Amer. Math. Soc., 98 (1961), 263284.Google Scholar
[7] Noether, E., Nichtkommutative Algebra, Math. Z., 37 (1933), 514541.CrossRefGoogle Scholar
[8] Osima, M., On the representations of groups of finite order, Math. J. Okayama Univ., 1 (1952), 3561.Google Scholar
[9] Osima, M., Note on blocks of group characters, Math. J. Okayama Univ., 4 (1955), 175188.Google Scholar
[10] Reynolds, W. F., A generalization of Brauer characters, Trans. Amer. Math. Soc., 119 (1965), 333351.Google Scholar
[11] Reynolds, W. F., Block idempotents of twisted group algebras, Proc. Amer. Math. Soc., 17 (1966), 280282.Google Scholar
[12] Rosenberg, A., Blocks and centres of group algebras, Math. Z., 76 (1961), 209216.Google Scholar
[13] Waerden, B. L. van der, Modern Algebra, vol. II, Frederick Ungar, New York, 1950.Google Scholar
[14] Yamazaki, K., On projective representations and ring extensions of finite groups, J. Fac Sci. Univ. Tokyo Sect. I, 10 (1964), 147195.Google Scholar