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- ...braic structures called groups. This introduction will rely heavily on set theory and [[modular arithmetic]] as well. Later on it will require an understandi After completing this section move on to [[Introduction to group theory/Part 2 Subgroups and cyclic groups]]. ...10 KB (1,788 words) - 07:02, 26 March 2022
- Let <math>G</math> be a group and let <math>a,b,c \in G</math> such that <math>ac=bc</math>. [[Category:Group theory]] ...481 bytes (101 words) - 09:28, 24 December 2022
- ...ein|''Albert Einstein'']] whose [[w:special theory of relativity|''special theory of relativity'']] is the main source of application. Photo taken by [[w:Pau ...e study of the infinite-dimensional unitary representations of the Lorentz group. These have both historical importance in mainstream physics, as well as c ...202 KB (29,362 words) - 01:43, 7 November 2020
- Let <math>G</math> be a group and let <math>g,a,b \in G</math> such that <math>a*g=e=g*a</math> and <math [[Category:Group theory]] ...257 bytes (57 words) - 09:28, 24 December 2022
- Let <math>G</math> be a group such that for all <math>a,b,c \in G</math> [[Category:Group theory]] ...413 bytes (76 words) - 09:27, 24 December 2022
- Let <math>G</math> be a group, and let <math>e,e' \in G</math> both be identity elements. [[Category:Group theory]] ...306 bytes (66 words) - 09:28, 24 December 2022
- Let <math>G</math> be a group and let <math>a,b \in G</math>. [[Category:Group theory]] ...342 bytes (81 words) - 09:28, 24 December 2022
- ...s a part of a group which forms under the same binary operation as per the group. [ Note: all elements of subgroup must be elements of groups] ...is said to be subgroup of G if , under the product in G, H itself forms a group. ...3 KB (658 words) - 20:27, 29 May 2024
- ...up'']] is named and [[Albert Einstein]] whose [[special relativity|special theory of relativity]] is the main source of application. Photo taken by [[w:Paul ...e study of the infinite-dimensional unitary representations of the Lorentz group. These have both historical importance in mainstream physics, as well as c ...201 KB (29,231 words) - 05:06, 16 December 2020
Page text matches
- Let <math>G</math> be a topological group regarded as a [[../CoIntersections/|topological]] space. Then <math>G</math> is defined to be a ''Polish group'' if it is also a Polish space. ...460 bytes (66 words) - 15:50, 12 September 2020
- ...../TrivialGroupoid/|topological group]]''; this is a [[../TrivialGroupoid/|group]] <math>(G, . ,e)</math> together == Definition: Topological Group == ...1 KB (174 words) - 16:15, 12 September 2020
- Let <math>G</math> be a group and let <math>g,a,b \in G</math> such that <math>a*g=e=g*a</math> and <math [[Category:Group theory]] ...257 bytes (57 words) - 09:28, 24 December 2022
- ...o X</math> is continuous). If <math>G</math> is a [[../PolishGroup/|Polish group]] and <math>X</math> is also a Polish space, then <math>X</math> is called ...Becker, Alexander S. Kechris. 1996. ''The Descriptive Set Theory of Polish Group Actions'' ...734 bytes (112 words) - 15:50, 12 September 2020
- Let <math>G</math> be a group such that for all <math>a,b,c \in G</math> [[Category:Group theory]] ...413 bytes (76 words) - 09:27, 24 December 2022
- #[[../CubicalHigherHomotopyGroupoid/|homotopy theory]] and [[../Pushout/|fundamental groups]] #Topology and [[../GroupoidHomomor #[[../CategoricalOntology/|category theory applications]] in algebraic topology ...3 KB (274 words) - 12:39, 6 May 2023
- Let <math>G</math> be a group and let <math>a,b \in G</math>. [[Category:Group theory]] ...342 bytes (81 words) - 09:28, 24 December 2022
- Let <math>G</math> be a group, and let <math>e,e' \in G</math> both be identity elements. [[Category:Group theory]] ...306 bytes (66 words) - 09:28, 24 December 2022
- ...let A and B be square matrices, and let α(s) and β(t) be paths in the Lie group of nonsingular matrices which satisfy ...1 KB (226 words) - 07:28, 22 August 2023
- Let <math>G</math> be a group and let <math>a,b,c \in G</math> such that <math>ac=bc</math>. [[Category:Group theory]] ...481 bytes (101 words) - 09:28, 24 December 2022
- A [[../TrivialGroupoid/|topological group]] <math>(G, . , e)</math> is metrizable if and only if <math>G</math> is Ha ...Becker, Alexander S. Kechris. 1996. ''The Descriptive Set Theory of Polish Group Actions. (London Mathematical Society Lecture Note Series)'' , Cambridge Un ...903 bytes (125 words) - 14:31, 8 October 2023
- #Symmetry and [[../TrivialGroupoid/|groups]] #Galois groups and Galois theory ...mFundamentalGroupoid/|fundamental groupoid functor]] #Extensions of Galois theory ...2 KB (188 words) - 16:15, 12 September 2020
- ...s a part of a group which forms under the same binary operation as per the group. [ Note: all elements of subgroup must be elements of groups] ...is said to be subgroup of G if , under the product in G, H itself forms a group. ...3 KB (658 words) - 20:27, 29 May 2024
- Every [[w:Graph theory|graph]] with [[w:Graph labeling|labeled]] knots has an [[w:Adjacency matrix |style="width: 50%;"| [[File:Symmetric group 4; Cayley graph 1,5,21 (Nauru Petersen); numbers.svg|400px]] ...2 KB (251 words) - 10:35, 20 August 2020
- ...rming the [[w:Lorentz group|Lorentz group]] or [[w:Poincaré group|Poincaré group]] preserving the [[w:Lorentz interval|Lorentz interval]] <math>-x_{0}^{2}+\ ...]] are [[w:Group isomorphism|isomorphic]] to the [[w:Lorentz group|Lorentz group]]. ...4 KB (542 words) - 09:39, 11 September 2023
- ...iewed as "adding the spatial notion of a `place' or location" to that of a group. In this context, the [[../HomotopyCategory/|homotopy category]] plays an i ...th that available for groups; such invertible operations also occur in the theory of inverse [[../TrivialGroupoid/|semigroups]]. Moreover, there are interest ...4 KB (501 words) - 04:59, 12 September 2020
- ...ebraic structure]]s such as [[monoid]]s, [[w:semigroup]]s, [[Abelian group|group]]s, [[groupoid]]s, [[rings]], [[module]]s, [[lattice]]s, or [[topological s ...]]s, and the essence of the mathematical theory of categories. or Category Theory, is often contained in natural transformations, such as natural equivalence ...4 KB (731 words) - 01:01, 20 August 2023
- ...tegory3/|non-Abelian]] character of the [[../HomotopyCategory/|fundamental group]] of a [[../CoIntersections/|topological]] space, or a novel approach to hi ...spaces and methods analogous to those used originally for the fundamental group or groupoid, obtains for example: ...3 KB (347 words) - 15:46, 12 September 2020
- ...lements and denote the range of the truth table values for the set and the group.<ref>See page 172 of the '''primary reference'''.</ref> ==== Group size ==== ...8 KB (1,161 words) - 20:13, 26 August 2020
- ...lements and denote the range of the truth table values for the set and the group.<ref>See page 172 of the '''primary reference'''.</ref> ==== Group size ==== ...8 KB (1,161 words) - 00:32, 26 August 2020