Geodesic
Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2
Canadian journal of mathematics, Tome 43 (1991) no. 4, pp. 792-813

Voir la notice de l'article provenant de la source Cambridge University Press

In his fundamental paper [1] J. L. Alperin introduced the idea of a weight in modular representation theory of finite groups G. Let p be a prime. A p-subgroup R is called a radical subgroup of G if R = Op (NG (R)). An irreducible character φ of NG (R) is called a weight character if φ is trivial on R and belongs to a p-block of defect zero of NG (R)/R. The G-conjugacy class of the pair (R, φ) is a weight of G. Let b be the p-block of NG (R) containing φ, and let B be p-block of G. A weight (R, φ) is a B-weight for the block B of G if B = bG , which means that B and b correspond under the Brauer homomorphism. Alperin's conjecture on weights asserts that the number l*(B) of B-weights of a p-block B of a finite group G equals the number l(B) of modular characters of B. 
Michler, G. O.; Olsson, J. B. Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2. Canadian journal of mathematics, Tome 43 (1991) no. 4, pp. 792-813. doi: 10.4153/CJM-1991-045-6
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[1] 1. Alperin, J.L., Weights for finite groups, The Areata Conference on Representations of Finite Groups, Proc. of Symposia in Pure Maths. 47(1987), 369–379. Google Scholar

[2] 2. Alperin, J.L., Fong, P., Weights for symmetric and general linear groups, J. Algebra 131(1990), 2–22. Google Scholar

[3] 3. Cabanes, M., Local structure of the p-blocks of S , Math. Z. 198(1988), 519–543. Google Scholar

[4] 4. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A., Atlas of finite groups. Clarendon Press, Oxford, 1985. Google Scholar

[5] 5. Feit, W., The representation theory of finite groups. North Holland, Amsterdam, 1982. Google Scholar

[6] 6. Gorenstein, D., Finite groups. Harper and Row, New York, 1968. Google Scholar

[7] 7. Humphreys, J.F., On certain projective modular representations of direct products, J. London Math. Soc. (2)32(1985), 449–459. Google Scholar

[8] 8. Isaacs, I.M., Character theory of finite groups. Academic Press, Noew York, 1976. Google Scholar

[9] 9. James, G., Kerber, A., The representation theory of the symmetric group. Addison-Wesley, London, 1981. Google Scholar

[10] 10. Michler, G.O., Ring theoretical and computational methods in group representation theory. Vorlesungen aus dem Fachbereich Mathematik der Universität Essen 18, 1989. Google Scholar

[11] 11. Michler, G.O., Olsson, J.B., The Alperin-McKay conjecture holds in the convering groups of symmetric and alternating groups, p≠2,J. reine angew. Math. 405(1990), 78–111. Google Scholar

[12] 12. Olsson, J.B., On the p-blocks of symmetric and alternating groups and their covering groups, J. Algebra 128(1990), 188–213. Google Scholar

[13] 13. Olsson, J.B., The number of modular characters of certain p-blocks, (to appear). Google Scholar

[14] 14. Schur, I., Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochenene lineare Substitutionen, J. reine angew. Math. 139(1911), 115–250. Google Scholar

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