# BN-pair

From Groupprops

## Contents |

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.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to BN-pair, all facts related to BN-pair) |Survey articles about this | Survey articles about definitions built on this

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View a list of other standard non-basic definitions

## Definition

### 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 :

and

Such a setup is also called a **Tits system** of rank .