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Template:BN-pair property
A BN-pair ( B , N ) {\displaystyle (B,N)} for a group G {\displaystyle G} is said to be split if B = ( B ∩ N ) U {\displaystyle B=(B\cap N)U} , where U {\displaystyle U} is a nilpotent normal subgroup of B {\displaystyle B} .
Any group of Lie type has a split BN-pair.
