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

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)

20-01 Instructional exposition (textbooks, tutorial papers, etc.)[edit]

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

Jtwdog 21:15, 28 October 2005 (UTC)

20A05 Axiomatics and elementary properties[edit]

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)
linas 23:45, 6 April 2007 (UTC)
I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)

20A99 Miscellaneous[edit]

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)

20Axx Foundations[edit]

20B05 General theory for finite groups[edit]

Jtwdog 21:31, 26 September 2005 (UTC)

20B15 Primitive groups[edit]

Jtwdog 21:31, 26 September 2005 (UTC)

20B20 Multiply transitive finite groups[edit]

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

20B30 Symmetric groups[edit]

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

20B35 Subgroups of symmetric groups[edit]

Jtwdog 18:21, 19 October 2005 (UTC)

20B40 Computational methods[edit]

20B99 Miscellaneous[edit]

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

20Bxx Permutation groups[edit]

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

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

20C08 Hecke algebras and their representations[edit]

20C15 Ordinary representations and characters[edit]

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)

20C30 Representations of finite symmetric groups[edit]

20C35 Applications of group representations to physics[edit]

20C99 Miscellaneous[edit]

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)

20Cxx Representation theory of groups[edit]

20D05 Classification of simple and nonsolvable groups[edit]

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

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

Jtwdog 04:09, 28 October 2005 (UTC)
Its a proof; added ref to simple group. linas 23:03, 6 April 2007 (UTC)

20D08 Simple groups: sporadic groups[edit]

Jtwdog 04:10, 28 October 2005 (UTC)

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[edit]

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

20D30 Series and lattices of subgroups[edit]

20D35 Subnormal subgroups[edit]

Jtwdog 23:49, 2 October 2005 (UTC)

20D60 Arithmetic and combinatorial problems[edit]

20D99 Miscellaneous[edit]

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)

20Dxx Abstract finite groups[edit]

20E05 Free nonabelian groups[edit]

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

linas 22:08, 6 April 2007 (UTC)
linas 22:30, 6 April 2007 (UTC)

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[edit]

Jtwdog 23:47, 2 October 2005 (UTC)

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

20E25 Local properties[edit]

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

20E26 Residual properties and generalizations[edit]

20E28 Maximal subgroups[edit]

20E32 Simple groups[edit]

20E34 General structure theorems[edit]

20E36 General theorems concerning automorphisms of groups[edit]

20E45 Conjugacy classes[edit]

Jtwdog 23:44, 2 October 2005 (UTC)

20E99 Miscellaneous[edit]

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

20Exx Structure and classification of infinite or finite groups[edit]

20F05 Generators, relations, and presentations[edit]

20F06 Cancellation theory; application of van Kampen diagrams[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[edit]

Jtwdog 23:38, 2 October 2005 (UTC)

20F19 Generalizations of solvable and nilpotent groups[edit]

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

Jtwdog 23:40, 2 October 2005 (UTC)

20F24 FC-groups and their generalizations[edit]

20F28 Automorphism groups of groups[edit]

20F34 Fundamental groups and their automorphisms[edit]

20F36 Braid groups; Artin groups[edit]

Jtwdog 04:12, 28 October 2005 (UTC)

20F38 Other groups related to topology or analysis[edit]

20F50 Periodic groups; locally finite groups[edit]

20F55 Reflection and Coxeter groups[edit]

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

20F60 Ordered groups[edit]

20F65 Geometric group theory[edit]

20F69 Asymptotic properties of groups[edit]

20F99 Miscellaneous[edit]

Jtwdog 04:14, 28 October 2005 (UTC)

20Fxx Special aspects of infinite or finite groups[edit]

20G15 Linear algebraic groups over arbitrary fields[edit]

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

AdamSmithee 09:42, 7 March 2006 (UTC)

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

20G40 Linear algebraic groups over finite fields[edit]

20Gxx Linear algebraic groups (classical groups)[edit]

20H05 Unimodular groups, congruence subgroups[edit]

20H20 Other matrix groups over fields[edit]

20Hxx Other groups of matrices[edit]

20J05 Homological methods in group theory[edit]

20J06 Cohomology of groups[edit]

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

20J15 Category of groups[edit]

20Jxx Connections with homological algebra and category theory[edit]

20K01 Finite abelian groups[edit]

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

Jtwdog 23:37, 2 October 2005 (UTC)

20K15 Torsion-free groups, finite rank[edit]

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

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

20K27 Subgroups[edit]

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

20K35 Extensions[edit]

20K99 Miscellaneous[edit]

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

20Kxx Abelian groups[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[edit]

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

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[edit]

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)

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

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

20M99 Miscellaneous[edit]

  • 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)

20Mxx Semigroups[edit]

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

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

20N05 Loops, quasigroups[edit]

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

20Nxx Other generalizations of groups[edit]