I know a presentation of the special linear group SL$(2,3)$(Presentation of ${\rm SL}(2,3)$). My question is that-
Can we give a presentation for SL$(n,\mathbb{Z}_p)$ in general or in more general can we give a presentation for SL$(n,\mathbb{F})$,where $\mathbb{F}$ is field.
As J.P. Serre had given presentation for SL$(2,\mathbb{Z})$
$$\mathrm{SL}_2(\mathbb{Z}) = \langle \,S, T \mid S^4 = 1, (ST)^3 = S^2 \,\rangle$$ where, \begin{align} S &= \begin{pmatrix} \phantom{-}0& 1 \\ -1 & 0 \end{pmatrix}, & T &= \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}. \end{align} I wants it to be more general.
There are presentations of $SL_n(K)$ for a field $K$, in particular for $K=\Bbb F_p$ and also for $SL_n(\Bbb Z)$. In the latter case we obtain this from the theory of arithmetic groups. The result is listed for $n\ge 3$, for example, in $5.6$, page 14 of the article An introduction to arithmetic groups by Christophe Soule: denote by $x_{ij}$ the matrices with diagonal elements $1$ and another entry $1$ at position $(i,j)$ and zero entries otherwise. Then we have $$ SL_n(\Bbb Z)=\langle x_{ij}, 1\le i\neq j\le n\mid [x_{ij},x_{kl}]=1 \text{ for } j\neq k, i\neq l,\; [x_{ij},x_{jk}]=x_{ik} \text{ for }i,j,k \text{ distinct }, (x_{12}x_{21}^{-1}x_{12})^4=1 \rangle $$ We can also generate the group by two elements only, but the relations then become very long. For the references see [6,9,20] in Soule's lecture notes.