Let C be a group with |C| = 44. Prove that C must contain an element of order 2.
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Q: Let C be a group with |C| = 44. Prove that Cmust contain an element of order 2.
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- Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.If p1,p2,...,pr are distinct primes, prove that any two abelian groups that have order n=p1p2...pr are isomorphic.Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.
- 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=x1y1z1.6. For each of the following values of , describe all the abelian groups of order , up to isomorphism. b. c. d. e. f.9. Suppose that and are subgroups of the abelian group such that . Prove that .