Geodesic
Modular Representations of Finite Groupswith Unsaturated Split (B,N)-Pairs
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 714-733

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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”.) 
Tinberg, N. B. Modular Representations of Finite Groupswith Unsaturated Split (B,N)-Pairs. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 714-733. doi: 10.4153/CJM-1980-056-x
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