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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.

This list will be periodically updated. Each entry in the list has three fields:

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N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
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20-00 General reference works (handbooks, dictionaries, bibliographies, etc.) edit

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

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

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

Jtwdog 21:15, 28 October 2005 (UTC)[reply]

20A05 Axiomatics and elementary properties edit

Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)[reply]
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
linas 23:45, 6 April 2007 (UTC)[reply]
I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)[reply]

20A99 Miscellaneous edit

Jtwdog 17:50, 26 October 2005 (UTC)[reply]
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)[reply]
Jtwdog 17:50, 26 October 2005 (UTC)[reply]
Jtwdog 17:50, 26 October 2005 (UTC)[reply]

20Axx Foundations edit

20B05 General theory for finite groups edit

Jtwdog 21:31, 26 September 2005 (UTC)[reply]

20B15 Primitive groups edit

Jtwdog 21:31, 26 September 2005 (UTC)[reply]

20B20 Multiply transitive finite groups edit

Jtwdog 19:48, 26 October 2005 (UTC)[reply]
Jtwdog 19:48, 26 October 2005 (UTC)[reply]
Jtwdog 19:48, 26 October 2005 (UTC)[reply]

20B30 Symmetric groups edit

Jtwdog 18:21, 19 October 2005 (UTC)[reply]
Jtwdog 18:21, 19 October 2005 (UTC)[reply]

20B35 Subgroups of symmetric groups edit

Jtwdog 18:21, 19 October 2005 (UTC)[reply]

20B40 Computational methods edit

20B99 Miscellaneous edit

Jtwdog 18:22, 19 October 2005 (UTC)[reply]
Jtwdog 18:22, 19 October 2005 (UTC)[reply]

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)[reply]
Jtwdog 20:26, 26 October 2005 (UTC)[reply]
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)[reply]
Jtwdog 20:26, 26 October 2005 (UTC)[reply]

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)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]

20Cxx Representation theory of groups edit

20D05 Classification of simple and nonsolvable groups edit

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

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

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

20D08 Simple groups: sporadic groups edit

Jtwdog 04:10, 28 October 2005 (UTC)[reply]

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)[reply]

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)[reply]
Done AdamSmithee 09:26, 7 March 2006 (UTC)[reply]
Oleg Alexandrov (talk) 04:15, 22 January 2007 (UTC)[reply]
AdamSmithee 09:28, 12 January 2006 (UTC)[reply]
NM after creation of the WP article - see above AdamSmithee 09:28, 12 January 2006 (UTC)[reply]
Actually, on a second thought, this is not a particularly illuminating proof. I linked to it AdamSmithee 09:26, 7 March 2006 (UTC)[reply]
AdamSmithee 09:28, 12 January 2006 (UTC)[reply]

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)[reply]
linas 22:30, 6 April 2007 (UTC)[reply]

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)[reply]

20E22 Extensions, wreath products, and other compositions edit

20E25 Local properties edit

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

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)[reply]

20E99 Miscellaneous edit

Jtwdog 23:46, 2 October 2005 (UTC)[reply]
Jtwdog 23:46, 2 October 2005 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]
Jtwdog 04:14, 28 October 2005 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]
Jtwdog 19:33, 1 November 2005 (UTC)[reply]
Jtwdog 19:33, 1 November 2005 (UTC)[reply]

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)[reply]

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)[reply]
Jtwdog 21:33, 26 September 2005 (UTC)[reply]
Jtwdog 21:33, 26 September 2005 (UTC)[reply]

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

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)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]

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

Jtwdog 23:27, 2 October 2005 (UTC)[reply]
Jtwdog 23:27, 2 October 2005 (UTC)[reply]
Jtwdog 23:27, 2 October 2005 (UTC)[reply]

20M99 Miscellaneous edit

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

20Mxx Semigroups edit

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

Jtwdog 23:24, 2 October 2005 (UTC)[reply]
Jtwdog 23:24, 2 October 2005 (UTC)[reply]

20N05 Loops, quasigroups edit

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

20Nxx Other generalizations of groups edit

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