Jump to content

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

Add links
From Wikipedia, the free encyclopedia

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:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

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]
[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]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Wikipedia:WikiProject_Mathematics/PlanetMath_Exchange/20-XX_Group_theory_and_generalizations&oldid=1136064983"