MCS-313 Extra Credit Problems
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Hand in by 10/9/00 for consideration
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If G is a group in which (ab)^i = a^i b^i for three consecutive integers
i for all a, b in G, show that G is Abelian.
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Suppose that G is a finite group with the property that every nonidentity
element has prime order (for example, D3 and D5).
If Z(G) is not trivial, prove that every nonidentity element of G has the
same order.
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Prove that an Abelian group of order 6 must be cyclic.
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