This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Definition with symbols
Let be a group. A pair of subgroups of is termed a BN-pair if it satisfies the following conditions:
- is generated by two subgroups and
- , viz the intersection is normal in the second subgroup
- is generated by involutions
- If is a coset representative of , then for each and every :
Such a setup is also called a Tits system of rank .