Let G be the symmetry group of a circle. Explain why G containsDn for all n.
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Let G be the symmetry group of a circle. Explain why G contains
Dn for all n.
Given: is the symmetry group of a circle.
We need to explain that contains
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- Construct a multiplication table for the group D5 of rigid motions of a regular pentagon with vertices 1,2,3,4,5.Assume that G is a finite group, and let H be a nonempty subset of G. Prove that H is closed if and only if H is subgroup of G.Exercises 38. Assume that is a cyclic group of order. Prove that if divides , then has a subgroup of order.