T tiasum2 May 2010 3 0 May 9, 2010 #1 Need help with a proof: Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p.

Need help with a proof: Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p.

Drexel28 MHF Hall of Honor Nov 2009 4,563 1,566 Berkeley, California May 9, 2010 #2 tiasum2 said: Need help with a proof: Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p. Click to expand... Hint 1: Spoiler Since \(\displaystyle G\) is abelian every subgroup is normal and so the only subgroups can be the trivial one or the full group. Hint 2: Spoiler If \(\displaystyle G\)'s only subgroups are the trivial one or the full group it is cyclic/

tiasum2 said: Need help with a proof: Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p. Click to expand... Hint 1: Spoiler Since \(\displaystyle G\) is abelian every subgroup is normal and so the only subgroups can be the trivial one or the full group. Hint 2: Spoiler If \(\displaystyle G\)'s only subgroups are the trivial one or the full group it is cyclic/