tag:blogger.com,1999:blog-12604614.post2733241577470737808..comments2017-03-10T02:08:06.554-08:00Comments on Math Refresher: Bertrand's Postulate (Theorem)Larry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-12604614.post-5871099399143847022010-06-03T15:22:08.367-07:002010-06-03T15:22:08.367-07:00Larry,
This isn't relevant to this post; I ho...Larry,<br /><br />This isn't relevant to this post; I hope you'll indulge me.<br /><br />I'm beginning to study abstract algebra for recreational purposes and I'm having trouble establishing whether a group is associative. <br /><br />Clearly, a counterexample shows when non-associativity. But how would I establish associativity? Right now, I'm looking at dihedral groups of symmetry and addition and multipliction modulo n.<br /><br />One idea I had for both of these is:<br />I make a Cayley table and each element shows up once in each column and row.<br /><br />take three elements x, y, z<br /><br />and begin with<br />(xy)z=x(yz)<br /><br />now xy = some product A<br />yz = some product B<br />xz= some product C<br /><br />this is three equations with three unknowns, x, y, and z, which can be solved based on the evidence from teh Cayley table<br /><br />Does this establish associativity?<br /><br />Thank you for your help.Sethhttp://www.blogger.com/profile/03602812642308936270noreply@blogger.com