Talk:Solvable group

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Mathematics rating:	Start Class	High Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs references. Geometry guy 00:05, 23 June 2007 (UTC)

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.

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"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)

I see, thankyou.Rich 16:41, 6 January 2007 (UTC)

[edit] Generalizations of soluble

I noticed I've been wanting articles that talk about pi-nilpotence, pi-separable, pi-soluble, pi-constrained, etc. This article already has supersoluble, but I wasn't sure if generalizations were also good. These terms are all basically defined in terms of normal series where the factors are restricted in some obvious way. For p-soluble for instance, it just means that the chief factors with order divisible by p are in fact p-groups (so elementary abelian p-groups). If this is not the right article for them, what would be? I don't like short stubs that just define a term. It is easier just to define the term within a larger article, but even better to group related definitions together and give context, relations, examples, etc. —Preceding unsigned comment added by JackSchmidt (talk • contribs) 06:38, 14 July 2007

[edit] Finite groups

For finite groups, do the notions solvable and supersolvable coincide? —Preceding unsigned comment added by 129.70.14.134 (talk) 22:24, 30 September 2007 (UTC)

No. The alternating group A₄ is solvable, but not supersolvable. --Zundark 07:57, 1 October 2007 (UTC)