# Generating specific matrix group in Sagemath

Hi, this is my first time here, and I am trying to use Sagemath to generate some matrix group.

The group I want to generate is the BLTA(Block Lower Triangular Group). For some background, the BLTA group has a parameter, called the **profile**, written as $\mathbf{s} = (s_1, s_2, \cdots s_l)$. The $\mathsf{BLTA}(\mathbf{s})$ group is a binary matrix group of size n by n where $n=s_1+s_2+\cdots+s_l$. We can consider this matrix as a block matrix with blocks divided by $s_1\times s_1, s_2\times s_2, \cdots s_l\times s_l$, and the lower trianglar part can be either 0 or 1, and the upper triangular part(excluding the main block diagonal) must be all zero. This forms a matrix group under ordinary matrix multiplication over the binary field $\mathbb{F}_2$. But I don't think I can find the generators of this group. How can I make this group in Sagemath?

**Edit** I realized that my description may be hard to understand due to my poor English skills. So essentially what I'm finding is a subgroup of the general linear group over the binary field $\mathbf{F}_2$ that has specific entries to be set to 0. But I am not aware of the generators of this new group. How can I implement it? I hope this makes more sense.

Can you provide an example of what you look for profile $(2,3)$, say? Also, what do you mean by saying

"I don't think I can find the generators of this group"? Didn't you just describe the generators?@Max Alekseyev So, for a profile with $\mathbf{s}=(2, 3)$, we are looking for a subset of 5 by 5 size matrices, and a generic element of this group would be $$ \begin{bmatrix} * & * & 0 & 0 & 0 \\ * & * & 0 & 0 & 0 \\ * & * & * & * & * \\ * & * & * & * & * \\ * & * & * & * & * \end{bmatrix} $$ where the star entries can be either 0 or 1, while ensuring that the matrix is invertible so that it is a subgroup of the general linear group.