BN-pair

Definition with symbols
Let $$G$$ be a group. A pair of subgroups $$B, N$$ of $$G$$ is termed a BN-pair if it satisfies the following conditions:


 * $$G$$ is generated by two subgroups $$B$$ and $$N$$
 * $$H : = B \cap N \triangleleft N$$, viz the intersection is normal in the second subgroup
 * $$W = N/H$$ is generated by involutions $$w_1,w_2,\ldots,w_m$$
 * If $$v_i$$ is a coset representative of $$w_i$$, then for each $$v \in N$$ and every $$i$$:

$$vBv_i \subseteq BvB \cup Bvv_iB$$ and $$v_iBv_i \not \subseteq B$$

Such a setup is also called a Tits system of rank $$m$$.