Stable general linear group

Summary

The stable general linear group $GL(R)$ of a ring $R$ is the union of all the general linear groups $GL_n(R)$. Each $GL_n(R)$ is placed inside the next by adding a $1$ on the diagonal. It is the group of invertible infinite matrices that differ from the identity in only finitely many entries. Algebraic K-theory starts from it: K1 of a ring is its abelianisation.