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Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2

Published online by Cambridge University Press:  20 November 2018

G. O. Michler  and
J. B. Olsson
G. O. Michler
Affiliation:
Institut für Experimentelle Mathematik, Universität GHS Essen, 4300 Essen 12, Germany
J. B. Olsson
Affiliation:
Matematisk Institut, København Universitet, 2100 København, Denmark
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 792 - 813
Copyright
Copyright © Canadian Mathematical Society 1991

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