Let E be an extension field of Z 2 and let E be algebraic of degree 3 over Z 2 Classify the groups (Z 2 (), ) and ((Z 2 ()) , ) according to the Fundamental Theorem of finitely generated abelian groups As usual, (Z 2 ()) is the set of nonzero elements of Z 2 () ...

The group Z 2 is abelian of order 8 with the property that a a 0 for ...

Let E be an extension field of Z 2 and let E be algebraic of

Question:

Let E be an extension field of Z₂ and let α ∈ E be algebraic of degree 3 over Z₂. Classify the groups (Z₂(α), +) and ((Z₂(α))*, ·) according to the Fundamental Theorem of finitely generated abelian groups. As usual, (Z₂(α))* is the set of nonzero elements of Z₂(α).

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