# Isomorphism between linear groups over field:F2

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Revision as of 15:33, 23 March 2012 by Vipul (talk | contribs) (Created page with "==Statement== Let <math>n</math> be a natural number. Then, we have isomorphisms between the following linear groups over field:F2: <math>GL(n,2) \cong SL(n,2) \cong...")

## 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