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Which of the following are groups? + And · denote the usual addition and multiplication of...

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Advance Math

Which of the following are groups? + And · denote theusual addition and multiplication of real numbers.

(G, +) with G = {2^ n | n ? Z},
(G, ·) with G = {2 ^n | n ? Z}.
Determine all subgroups of the following cyclic group
G = {e, a, a^2, a^3, a^4, a^5}.
Which of these subgroups is a normal divisor of G?

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