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0 $begingroup$ Proof Let G be a group of order 6. By Lagrange's Theorem, G has subgroups of order 1,2,3 and 6. The subgroups of orders 2 and 3 have prime orders and are cyclic therefor. The subgroup contains an element g of order 2 and the subgroup contains an element h of order 3. So therefore G is cyclic. Is this correct or is there also proof of group G not being cyclic abstract-algebra group-theory cyclic-groups share | cite | improve this question edited Dec 3 '18 at 4:26 Kemono Chen 2,918 1 7 39 asked Dec