Given a group G, non-abelian, with |G|= , show G has distinct conjugacy classes.

Any help would be great -- I'm sure there's a useful theorem or fact I'm missing out on.

thanks!

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- Apr 4th 2010, 08:36 PMkimberuFinding the number of conjugacy classes
Given a group G, non-abelian, with |G|= , show G has distinct conjugacy classes.

Any help would be great -- I'm sure there's a useful theorem or fact I'm missing out on.

thanks! - Apr 4th 2010, 11:21 PMNonCommAlg
- Apr 5th 2010, 12:06 AMkimberu
So the class equation says:

http://planetmath.org/js/jsmath/font...144/char6A.pngGhttp://planetmath.org/js/jsmath/font...144/char6A.png=http://planetmath.org/js/jsmath/font...144/char6A.pngZ(G)http://planetmath.org/js/jsmath/font...144/char6A.png+http://planetmath.org/js/jsmath/font...144/char50.png[G:C( )]

meaning,

this sum, but what exactly is the sum? Is it just p, m times? (sorry, I've never used this equation before. thanks so much for the help!) - Apr 5th 2010, 12:13 AMNonCommAlg