MCS-313 Extra Credit Problems
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Hand in by 9/27/00 for consideration
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Show that if G is a finite group with identity e and with an even number
of elements, then there is an element b not equal to e in G such that b2
= e. Show that the number of elements of G of order 2 is odd.
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Let G be a nonempty set closed under an associative product, which in addition
satisfies:
(a)There exists and e in G such that a*e = a for all a in G. (right
identity)
(b) Given a in G, there exists an element y in G such that a*y = e.
(right inverses)
Prove that G is a group.
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