If a group G has only three elements, show that it must be abelian.
1
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
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
"assignmentexpert.com" is professional group of people in Math subjects! They did assignments in very high level of mathematical modelling in the best quality. Thanks a lot
Comments
Leave a comment