# Isomorphism between linear groups over field:F2

## Statement

Let be a natural number. Then, we have isomorphisms between the following linear groups over field:F2:

where the isomorphisms arise from the usual subgroup, quotient and subquotient maps that relate these groups. In particular:

- The embedding of the subgroup in is an isomorphism, i.e., the subgroup is the whole group
- The quotient map from to is an isomorphism, i.e., the kernel is trivial
- The embedding of in is an isomorphism, i.e., the subgroup is the whole group
- The quotient map from to is an isomorphism, i.e., the kernel is trivial