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- True or False Label each of the following statements as either true or false. Disjoint cycles commute under mapping composition.Find the right regular representation of G as defined Exercise 11 for each of the following groups. a. G={ 1,i,1,i } from Example 1. b. The octic group D4={ e,,2,3,,,, }.Label each of the following statements as either true or false. Let x,y, and z be elements of a group G. Then (xyz)1=x1y1z1.
- Label each of the following statements as either true or false. Two groups can be isomorphic even though their group operations are different.Let a and b be elements of a group G. Prove that G is abelian if and only if (ab)2=a2b2.Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?