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Homework Help
Calculus and Beyond Homework Help
Prove a semigroup is a group
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[QUOTE="TheFurryGoat, post: 2882053, member: 198995"] [h2]Homework Statement [/h2] Prove, that a senigruop S is a group if and only if for every x in S there exists a unique x' in S so that xx'x=x. [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] I am trying to prove that xx'=1[SUB]S[/SUB] for all x in S. But all I can show is that xx' is in E[SUB]S[/SUB]={x | x^2=x} for every x in S. I am having a lot of troubles proving xx'=yy' and I can't even prove that 1[SUB]S[/SUB] si in S. Am I going in the right direction? [/QUOTE]
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Prove a semigroup is a group
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