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How do you find proper subgroups of a cyclic group of order 6?
Wiki User
∙ 10y ago
A cyclic group of order 6 is isomorphic to that generated by elements a and b where a2 = 1, b3 = 1, or to the group generated by c where c6 = 1.
So, find the identity element, 1.
Next find an element which when operated on by itself, equals the identity. This element will correspond to a or c3.
Finally find an element which when operated on by itself twice (so that it is cubed or multiplied by 3), equals the identity. This element will correspond to b or c2.
The subgroups {1}, (1, a} = {1, c3} and {1, b, b2} = {1, c2, c4} will be proper subgroups.
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∙ 10y ago
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