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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?

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?