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Prove that there is only one possible multiplication table for G if G has exactly 1,...

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Advance Math

  1. Prove that there is only one possible multiplication table forG if G has exactly 1, 2, or 3 elements. Analyze the possiblemultiplication tables for groups with exactly 4 elements, and showthat there are two distinct tables, up to reordering the elementsof G. Use these tables to prove that all groups with < 4elements are commutative.

(You are welcome to analyze groupswith 5 elements using the same technique, but you will soon knowenough about groups to be able to avoid such brute-forceapproaches.)

Answer & Explanation Solved by verified expert
3.8 Ratings (518 Votes)
If G has exactly one element say then we must have the groupidentity and so the table is    See Answer
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