Let G be a group and let x ∈ G. Prove that if a has order of 12, then x3 has order 4.
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Let G be a group and let x ∈ G. Prove that if a has order of 12, then x3 has order 4.
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- 18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .Let be a group of order , where and are distinct prime integers. If has only one subgroup of order and only one subgroup of order , prove that is cyclic.