If a group G has only three elements, show that it must be abelian.
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Expert's answer
2012-12-24T11:20:19-0500
As G is a group (with elements a,b,c), there must beidentity element among a b and c. Let it be a. That means ab=ba=b ac=ca=c For other elements there must be inverse to them insidegroup. It easy to understand that b and c are inverse each to other as a is identity element we have b^(-1) = c bc=cb=a Thus, we just show that group G is abelian as for any 2elements g1, g2 we have g1g2=g2g1
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