Isomorphism between linear groups over field:F2
From Groupprops
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