Stable elementary subgroup
= Stable elementary subgroup
{title2=$E_\infty(A)=\langle I+ae_{ij}:i\ne j\rangle$}
The subgroup generated by elementary <transvections> in finite <matrix> sizes, with identity stabilization. A third distinct index expresses each <transvection> as a commutator; stable block identities show that this subgroup is normal and that its quotient in the <stable general linear group> is abelian. Thus it is precisely the <commutator subgroup>.