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- ...eorem''' in [[group theory]] states if G is a finite [[group (mathematics)|group]] and H is a [[subgroup]] of G, then |H| (how many elements are in H, calle * For any g in a group G, <math>g^k=e</math> for some k that divides the |G| ...671 bytes (112 words) - 23:46, 5 July 2023
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- ...eorem''' in [[group theory]] states if G is a finite [[group (mathematics)|group]] and H is a [[subgroup]] of G, then |H| (how many elements are in H, calle * For any g in a group G, <math>g^k=e</math> for some k that divides the |G| ...671 bytes (112 words) - 23:46, 5 July 2023
- ...up theory]], a branch of [[mathematics]], a subgroup <math>N</math> of the group <math>G</math> is normal in <math>G</math> if and only if <math>\frac{1}{gn [[Category:Group theory]] ...359 bytes (64 words) - 23:46, 5 July 2023
- ...p''' of ''<math>G</math>'' if the elements ''<math>H</math>'' also forms a group under the binary operation. [[Category:Group theory]] ...597 bytes (103 words) - 18:10, 15 June 2024
- ...matics]], specifically [[group theory]], the sporadic groups are a type of group which cannot be classified into any of the infinite families of simple grou There are 26 sporadic groups, the biggest being the [[Monster group]] (or Fischer-Griess monster), with a [[cardinality]] of approx. <math>8.1\ ...2 KB (265 words) - 13:51, 29 June 2024
- ...\}</math> is the set of all cosets of N in G and is called the '''quotient group''' of N in G. This group is used in the proof of [[Lagrange's Theorem]], for instance. In fact, the ...575 bytes (101 words) - 21:35, 1 October 2023
- ...ve]]. Because of that, an abelian group is sometimes called a ‘commutative group’. ...ion is not commutative is called a ‘non-abelian group’ or ‘non-commutative group’. ...2 KB (303 words) - 12:41, 23 July 2023
- The '''kernel''' of a [[group homomorphism]] from ''G'' to ''H'' is the subset of the elements from ''G'' Mathematically: <math> \ker f = \{g \in G : f(g) = e_{H}\}</math>. Since a group homomorphism preserves identity elements, the [[identity element]] of ''G'' ...1 KB (214 words) - 06:20, 4 November 2022
- In [[number theory]], the '''totient''' of a [[positive number|positive]] [[integer]] ''n'' is ...}/n\mathbb{Z}</math>. This fact, together with [[Lagrange's theorem (group theory)|Lagrange's theorem]], provides a proof for [[Euler's theorem]]. ...2 KB (375 words) - 16:55, 14 August 2024
- :''This article is about the basic notions. For advanced topics, see [[Group theory]].'' ...s Revenge]] cube. Turns of the sides make the positions of the cube into a group.]] ...11 KB (1,752 words) - 16:07, 18 January 2025
- ...st2=Barry|date=2021|title=Numbers and properties|journal=Journal of Number Theory}}</ref> ...t of Mathematics. Chair of Pure Mathematics. Algebra and Calculus Research Group|date=2020-09-30|degree=info:eu-repo/semantics/bachelorThesis|language=en|fi ...1 KB (205 words) - 15:34, 10 October 2024
- ...onnection between [[Field (mathematics)|field]]s and [[Group (mathematics)|group]]s. Galois theory gives a concrete connection between hard-to-study fields and easy-to-study ...8 KB (1,283 words) - 12:08, 23 September 2024
- All the elements <math>1, 2, \ldots, 6</math> of the group modulo 7 can be expressed that way. The number 2 is no primitive root modul [[Category:Number theory]] ...708 bytes (101 words) - 14:54, 12 April 2017
- ...ning an [[elliptic curve]]. It is an open problem in the field of [[number theory]]. It is one of the most challenging mathematical problems, although the mo ...al and the other irrational. The set of rational solutions is an [[abelian group]]. This means that given rational points <math>P</math> and <math>Q</math>, ...2 KB (280 words) - 15:16, 24 October 2024
- ...pt]] were by [[R.A. Fisher]] in 1930,<ref>{{cite book |title=The genetical theory of natural selection |url=https://archive.org/details/geneticaltheoryo03163 ...dual.<ref>{{cite journal |last=Maynard Smith |first=John |year=1964 |title=Group selection and kin selection |journal=Nature |volume=201 |issue=4924 |pages= ...4 KB (571 words) - 18:10, 10 October 2023
- ...g Cantor]]. <math>\aleph_0</math> is the number of numbers that are in the group 0, 1, 2, 3, ... (which goes on forever). Both the set of [[Natural number|n [[Category:Number theory]] ...2 KB (356 words) - 23:30, 12 July 2022
- ...olecular orbital]]s. This is used in the [[Hückel method]], [[ligand field theory]], and the [[Woodward–Hoffmann rules]]. Another idea on a larger scale is t ...ic point groups was published in 1936 by Rosenthal and Murphy.<ref>''Group Theory and the Vibrations of Polyatomic Molecules'' Jenny E. Rosenthal and G. M. M ...19 KB (2,977 words) - 11:37, 25 September 2024
- ...llowing the name of the group is the [[order (group theory)|order]] of the group. !colspan=2 | [[Coxeter group|Symmetry group]] ...8 KB (1,038 words) - 19:54, 31 January 2024
- ...r of samples of various distributions.<ref>Gumbel, E.J. 1954. "Statistical theory of extreme values and some practical applications". ''Applied Mathematics S ...the blue group has a larger ''standard deviation'' (SD=σ=50) than the red group (SD=σ=10).]] ...6 KB (871 words) - 00:16, 19 January 2025
- ...am.com|language=en}}</ref> (<math>\mathbf{Z}</math>, +, 0) is an [[abelian group]]. [[Category:Number theory]] ...2 KB (327 words) - 04:47, 18 December 2024
- ...-H bond, which now acts as a proton donor under [[Brønsted-Lowry acid-base theory]] to release the hydrogen as a H+ ion, increasing the acidity of the soluti ...2 KB (344 words) - 11:55, 1 July 2024