Upper unitriangular group
= Upper unitriangular group
The upper unitriangular group consists of upper triangular matrices with every diagonal entry equal to one. Over $\mathbb F_p$ it has order $p^{n(n-1)/2}$ and is a <Sylow subgroup> of $GL_n(\mathbb F_p)$.
Its elements form the upper triangular, diagonal-one subset of <triangular matrices>.