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Unformatted text preview: the inverse map possibly be except left multiplication by a 1 ? So lets try that. We have L a 1 .L a .x// D a 1 .ax/ D .a 1 a/x D ex D x; so L a 1 L a D id G . A similar computation shows that L a L a 1 D id G . This shows that L a and L a 1 are inverse maps, so both are bijective. The proof for R a is similar. n Corollary 2.1.6. Let G be a group and let a and b be elements of G . The equation ax D b has a unique solution x in G , and likewise the equation xa D b has a unique solution in G ....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08