Could someone explain why being simple and abelian implies it's cyclic? Thanks! -Chip
Last edited by chiph588@; Apr 11th 2010 at 05:05 PM.
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Originally Posted by chiph588@ Could someone explain why simple and abelian implies it is cyclic? Thanks! -Chip choose then is a non-trivial normal subgroup of because is abelian. so because is simple.
Originally Posted by NonCommAlg choose then is a non-trivial normal subgroup of because is abelian. so because is simple. Ah yes this proof was rather... *takes glasses off* simple.
Originally Posted by chiph588@ Ah yes this proof was rather... *takes glasses off* simple. G should be finite though.
Originally Posted by aliceinwonderland G should be finite though. of coures, infinite abelian group are never simple. also, obviously, the finite ones are either of order 1 or a prime number.
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