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Show that Z/2Z × Z/nZ is cyclic if and only if n is even. Abstract Algebra

Show that Z/2Z × Z/nZ is cyclic if and only if n is even.

Abstract Algebra

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Answer #1

So, by the above question Z/2Z x Z/nZ is cyclic if and only if gcd(n,2) = 1

So, gcd(2,n) = 1 implies n must be odd.

Note that, the question is wrong. The correct framing should be, Show that Z/2Z × Z/nZ is cyclic if and only if n is "ODD"

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