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Modular Representations of Finite Groupswith Unsaturated Split (B,N)-Pairs

Published online by Cambridge University Press:  20 November 2018

N. B. Tinberg
N. B. Tinberg*
Affiliation:
Occidental College, Los Angeles, California
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1. Introduction.Let p be a prime number. A finite group G = (G, B, N, R, U) is called a split(B, N)-pair of characteristic p and rank n if

(i) G has a (B, N)-pair (see [3, Definition 2.1, p. B-8]) where H= B ⋂ N and the Weyl group W= N/H is generated by the set R= ﹛ω 1,… , ω n) of “special generators.”

(ii) H= ⋂n∈N n-1Bn

(iii) There exists a p-subgroup U of G such that B = UH is a semidirect product, and H is abelian with order prime to p.

A (B, N)-pair satisfying (ii) is called a saturated (B, N)-pair. We call a finite group G which satisfies (i) and (iii) an unsaturated split (B, N)- pair. (Unsaturated means “not necessarily saturated”.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 3 , 01 June 1980 , pp. 714 - 733
Copyright
Copyright © Canadian Mathematical Society 1980

References

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