I understand how {1} and {5} are generators of Z6.(adsbygoogle = window.adsbygoogle || []).push({});

{1} = {1, 2, 3, 4, 5, 0} = {0, 1, 2, 3, 4, 5}

{5} = {5, 4, 3, 2, 1, 0} = {0, 1, 2, 3, 4, 5}

But my book also says that {2, 3} also generates Z6 since 2 + 3 = 5 such as {2,3,4} and {3,4} I believe. Thus every subgroup containing 2 and 3 must also be 5 except for {2,4}.

Can someone explain this to me? Ty in advance.

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# Generators of Z6

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