Suppose that G is a group with the property that for every choice of elements in G, axb = cxd but ab = cd. Prove that G is Abelian. ?
("Middle cancellation" implies commutativity.)
In a finite group, show that the number of nonidentity elements that satisfy the equation x^5 = e is a multiple of 5.?
If the stipulation that the group be finite is omitted, what can you say about the number of nonidentity elements that satisfy the equation x^5 = e?
(1) x = -3t2 + 4t - 2 and y = 6t2- 4t
(2) x = - 3t3 - 4t and y = -5t2 + 6
(3) r = 2t2i – (4t+3) j
(4) r = (4t3– 2t) i +3 j
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