Wikipedia:WikiProject Mathematics/PlanetMath Exchange/20-XX Group theory and generalizations

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This page provides a list of all articles available at PlanetMath in the following topic:

20-XX Group theory and generalizations.

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[edit] 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

Jtwdog 16:55, 20 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
AdamSmithee 09:01, 12 January 2006 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
Jtwdog 18:08, 19 October 2005 (UTC)
AdamSmithee 08:47, 7 March 2006 (UTC)

[edit] 20-02 Research exposition (monographs, survey articles)

Jtwdog 21:15, 28 October 2005 (UTC)

[edit] 20A05 Axiomatics and elementary properties

Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 18:17, 19 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
Jtwdog 17:26, 20 October 2005 (UTC)
I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)

[edit] 20A99 Miscellaneous

Jtwdog 17:50, 26 October 2005 (UTC)
Some work needs to be done here to draw the distinctions between direct sum and direct product. Merging together the two articles might be a good idea. Jtwdog 17:50, 26 October 2005 (UTC)
Jtwdog 17:50, 26 October 2005 (UTC)
Jtwdog 17:50, 26 October 2005 (UTC)

[edit] 20B05 General theory for finite groups

Jtwdog 21:31, 26 September 2005 (UTC)

[edit] 20B15 Primitive groups

Jtwdog 21:31, 26 September 2005 (UTC)

[edit] 20B20 Multiply transitive finite groups

Jtwdog 19:48, 26 October 2005 (UTC)
Jtwdog 19:48, 26 October 2005 (UTC)
Jtwdog 19:48, 26 October 2005 (UTC)

[edit] 20B30 Symmetric groups

Jtwdog 18:21, 19 October 2005 (UTC)
Jtwdog 18:21, 19 October 2005 (UTC)

[edit] 20B35 Subgroups of symmetric groups

Jtwdog 18:21, 19 October 2005 (UTC)

[edit] 20B99 Miscellaneous

Jtwdog 18:22, 19 October 2005 (UTC)
Jtwdog 18:22, 19 October 2005 (UTC)

[edit] 20C05 Group rings of finite groups and their modules

[edit] 20C07 Group rings of infinite groups and their modules

[edit] 20C15 Ordinary representations and characters

It's nice to include counter-examples, though this is probably a low priority. Jtwdog 20:26, 26 October 2005 (UTC)
Jtwdog 20:26, 26 October 2005 (UTC)
It would be nice to bring over a little of the proof, as I think it's quite beautiful, but I'll leave that to other's judgement.Jtwdog 20:26, 26 October 2005 (UTC)
Jtwdog 20:26, 26 October 2005 (UTC)

[edit] 20C30 Representations of finite symmetric groups

[edit] 20C99 Miscellaneous

Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)
Jtwdog 04:08, 28 October 2005 (UTC)

[edit] 20D05 Classification of simple and nonsolvable groups

Oleg Alexandrov (talk) 23:05, 21 November 2005 (UTC)

[edit] 20D06 Simple groups: alternating groups and groups of Lie type

Jtwdog 04:09, 28 October 2005 (UTC)

[edit] 20D08 Simple groups: sporadic groups

Jtwdog 04:10, 28 October 2005 (UTC)

[edit] 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks

[edit] 20D15 Nilpotent groups, $p$-groups

[edit] 20D20 Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

  • PM: p-subgroup, id=5184 -- WP guess: p-subgroup -- Status:

[edit] 20D25 Special subgroups (Frattini, Fitting, etc.)

[edit] 20D30 Series and lattices of subgroups

[edit] 20D35 Subnormal subgroups

Jtwdog 23:49, 2 October 2005 (UTC)

[edit] 20D60 Arithmetic and combinatorial problems

[edit] 20D99 Miscellaneous

The ling is currently redirecting to Order (group theory), which mentions the theorem in passing (anyway, the article should be cleaned up). I think that something more like Lagrange's theorem (group theory) would be more appropriate AdamSmithee 09:28, 12 January 2006 (UTC)
Done AdamSmithee 09:26, 7 March 2006 (UTC)
Oleg Alexandrov (talk) 04:15, 22 January 2007 (UTC)
AdamSmithee 09:28, 12 January 2006 (UTC)
NM after creation of the WP article - see above AdamSmithee 09:28, 12 January 2006 (UTC)
Actually, on a second thought, this is not a particularly illuminating proof. I linked to it AdamSmithee 09:26, 7 March 2006 (UTC)
AdamSmithee 09:28, 12 January 2006 (UTC)

[edit] 20E05 Free nonabelian groups

[edit] 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

[edit] 20E07 Subgroup theorems; subgroup growth

[edit] 20E10 Quasivarieties and varieties of groups

[edit] 20E15 Chains and lattices of subgroups, subnormal subgroups

[edit] 20E18 Limits, profinite groups

Jtwdog 23:47, 2 October 2005 (UTC)

[edit] 20E22 Extensions, wreath products, and other compositions

[edit] 20E25 Local properties

Oleg Alexandrov (talk) 04:17, 22 January 2007 (UTC)

[edit] 20E26 Residual properties and generalizations

[edit] 20E32 Simple groups

[edit] 20E34 General structure theorems

[edit] 20E36 General theorems concerning automorphisms of groups

[edit] 20E45 Conjugacy classes

Jtwdog 23:44, 2 October 2005 (UTC)

[edit] 20E99 Miscellaneous

Jtwdog 23:46, 2 October 2005 (UTC)
Jtwdog 23:46, 2 October 2005 (UTC)

[edit] 20F05 Generators, relations, and presentations

[edit] 20F10 Word problems, other decision problems, connections with logic and automata

[edit] 20F12 Commutator calculus

[edit] 20F14 Derived series, central series, and generalizations

[edit] 20F16 Solvable groups, supersolvable groups

[edit] 20F18 Nilpotent groups

Jtwdog 23:38, 2 October 2005 (UTC)

[edit] 20F19 Generalizations of solvable and nilpotent groups

[edit] 20F22 Other classes of groups defined by subgroup chains

Jtwdog 23:40, 2 October 2005 (UTC)

[edit] 20F24 FC-groups and their generalizations

[edit] 20F28 Automorphism groups of groups

[edit] 20F36 Braid groups; Artin groups

Jtwdog 04:12, 28 October 2005 (UTC)

[edit] 20F50 Periodic groups; locally finite groups

[edit] 20F55 Reflection and Coxeter groups

Jtwdog 04:14, 28 October 2005 (UTC)
Jtwdog 04:14, 28 October 2005 (UTC)

[edit] 20F60 Ordered groups

[edit] 20F65 Geometric group theory

[edit] 20F69 Asymptotic properties of groups

[edit] 20F99 Miscellaneous

Jtwdog 04:14, 28 October 2005 (UTC)
  • PM: Hopfian group, id=7516new! -- WP guess: Hopfian group -- Status:

[edit] 20G15 Linear algebraic groups over arbitrary fields

[edit] 20G20 Linear algebraic groups over the reals, the complexes, the quaternions

AdamSmithee 09:42, 7 March 2006 (UTC)

[edit] 20G25 Linear algebraic groups over local fields and their integers

[edit] 20G40 Linear algebraic groups over finite fields

[edit] 20H05 Unimodular groups, congruence subgroups

[edit] 20H20 Other matrix groups over fields

[edit] 20J05 Homological methods in group theory

[edit] 20J06 Cohomology of groups

Jtwdog 19:33, 1 November 2005 (UTC)
Jtwdog 19:33, 1 November 2005 (UTC)
Jtwdog 19:33, 1 November 2005 (UTC)

[edit] 20J15 Category of groups

[edit] 20K01 Finite abelian groups

[edit] 20K10 Torsion groups, primary groups and generalized primary groups

Jtwdog 23:37, 2 October 2005 (UTC)

[edit] 20K20 Torsion-free groups, infinite rank

[edit] 20K25 Direct sums, direct products, etc.

[edit] 20K27 Subgroups

[edit] 20K30 Automorphisms, homomorphisms, endomorphisms, etc.

[edit] 20K99 Miscellaneous

Jtwdog 21:33, 26 September 2005 (UTC)
Jtwdog 21:33, 26 September 2005 (UTC)
Jtwdog 21:33, 26 September 2005 (UTC)

[edit] 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)

[edit] 20M05 Free semigroups, generators and relations, word problems

[edit] 20M10 General structure theory

  • PM: ideal, id=3516 -- WP guess: ideal -- Status:
  • PM: Rees factor, id=3517 -- WP guess: Rees factor -- Status:

[edit] 20M12 Ideal theory

[edit] 20M14 Commutative semigroups

[edit] 20M17 Regular semigroups

[edit] 20M18 Inverse semigroups

[edit] 20M20 Semigroups of transformations, etc.

[edit] 20M30 Representation of semigroups; actions of semigroups on sets

Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)
Jtwdog 23:35, 2 October 2005 (UTC)

[edit] 20M35 Semigroups in automata theory, linguistics, etc.

Jtwdog 23:27, 2 October 2005 (UTC)
Jtwdog 23:27, 2 October 2005 (UTC)
Jtwdog 23:27, 2 October 2005 (UTC)

[edit] 20M99 Miscellaneous

  • PM: band, id=3319 -- WP guess: band -- Status:
AdamSmithee 09:35, 12 January 2006 (UTC)
  • PM: rig, id=6378 -- WP guess: rig -- Status:
AdamSmithee 09:35, 12 January 2006 (UTC)
AdamSmithee 09:35, 12 January 2006 (UTC)

[edit] 20N02 Sets with a single binary operation (groupoids)

Jtwdog 23:24, 2 October 2005 (UTC)
Jtwdog 23:24, 2 October 2005 (UTC)

[edit] 20N05 Loops, quasigroups

Oleg Alexandrov (talk) 04:18, 22 January 2007 (UTC)
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