nLab
BN-pair
Contents
Context
Group Theory
group theory
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Contents
Definition
A pair of subgroups of a group is a BN-pair if the following holds:
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the union generates ,
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the intersection is a normal subgroup of ,
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the quotient group is generated by a set of involutions,
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for each we have
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for ,
Note that the set is uniquely determined by these axioms, and that is a Coxeter system.
References
Last revised on October 25, 2020 at 13:54:13.
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