Talk:Solvable group
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Polya's dictum : "if there's a problem you can't figure out, there's a simpler problem you can't (?) figure out" seems wrong. Moreover, the opposite sentence "if there's a problem you can't figure out, there's a simpler problem you can figure out" is obviously a reformulation from the works of René Descartes.
"as every simple, abelian group must be cyclic of prime order" seems to be wrong; actually as every simple, abelian group must be products of cyclic groups (may not be of prime order).
- Every simple abelian group is cyclic of prime order. For an abelian group to be simple it must not have any proper non-trivial subgroups, because all its subgroups are normal. --Zundark 07:49, 9 Apr 2004 (UTC)
Zundark's right
[edit] I think S3 Is nilpotent.
Every commutater is of course even. So the commutator subgroup is A3. Am I missing something?Rich 10:06, 6 January 2007 (UTC)
- The commutator subgroup of S3 is indeed A3. The next term of the lower central series of S3 is also A3. So S3 is not nilpotent. --Zundark 11:30, 6 January 2007 (UTC)
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- I see, thankyou.Rich 16:41, 6 January 2007 (UTC)
