Group theory

Subgroup method

The subgroup method is an algorithm used in the mathematical field of group theory. It is used to find the word of an element. It doesn't always return the minimal word, but it can return optimal words based on the series of subgroups that is used. The code looks like this: function operate(element, generator) function subgroup(g) sequence := (set of subgroups that will be used, depending on the method.) word := [] for subgroup in sequence coset_representatives := [] for operation in coset_representatives if operate(g, operation) is in the next subgroup then append operation onto word g = operate(g, operation) break return word * v * t * e * v * t * e (Wikipedia).

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Subgroups abstract algebra

In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.

From playlist Abstract algebra

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Definition of a Subgroup in Abstract Algebra with Examples of Subgroups

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Subgroup in Abstract Algebra with Examples of Subgroups

From playlist Abstract Algebra

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Abstract Algebra | Cyclic Subgroups

We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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All About Subgroups | Abstract Algebra

We introduce subgroups, the definition of subgroup, examples and non-examples of subgroups, and we prove that subgroups are groups. We also do an example proving a subset is a subgroup. If G is a group and H is a nonempty subset of G, we say H is a subgroup of G if H is closed with respect

From playlist Abstract Algebra

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GT2. Definition of Subgroup

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

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Abstract Algebra | The notion of a subgroup.

We present the definition of a subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Statistics: Sampling Methods

This lesson introduces the different sample methods when conducting a poll or survey. Site: http://mathispower4u.com

From playlist Introduction to Statistics

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Research Methods 1: Sampling Techniques

In this video, I discuss several types of sampling: random sampling, stratified random sampling, cluster sampling, systematic sampling, and convenience sampling. The figures presented are adopted/adapted from: https://www.pngkey.com/detail/u2y3q8q8e6o0u2t4_population-and-sample-graphic-de

From playlist Research Methods

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Definition of a group Lesson 24

In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

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GAP - 5 by Alexander Hulpke

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

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Bettina EICK - Computational group theory, cohomology of groups and topological methods 5

The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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GAP - 4 by Alexander Hulpke

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

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Visual Group Theory, Lecture 3.4: Direct products

Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and mu

From playlist Visual Group Theory

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Free Group Rings by I. B. S. Passi

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

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Computing Wedderburn decomposition using the concept of Shoda pairs by Sugandha Maheshwari

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

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Mazur's program B. - Zureick-Brown - Workshop 2 - CEB T2 2019

David Zureick-Brown (Emory University, Atlanta USA) / 25.06.2019 Mazur's program B. I’ll discuss recent progress on Mazur’s “Program B” – the problem of classifying all possibilities for the “image of Galois” for an elliptic curve over Q (equivalently, classification of all rational poi

From playlist 2019 - T2 - Reinventing rational points

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Werner Muller - Asymptotics of automorphic spectra and the trace formula

December 18, 2014 - Analysis, Spectra, and Number theory: A conference in honor of Peter Sarnak on his 61st birthday. In this talk I will discuss the asymptotic behaviour of the discrete (resp. cuspidal) spectrum of arithmetic groups with respect to the growth of various parameters such

From playlist Analysis, Spectra, and Number Theory - A Conference in Honor of Peter Sarnak on His 61st Birthday

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Angelica Babei - A family of $\phi$-congruence subgroups of the modular group

In this talk, we introduce families of subgroups of finite index in the modular group, generalizing the congruence subgroups. One source of such families is studying homomorphisms of the modular group into linear algebraic groups over finite fields. In particular, we examine a family of no

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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Definition of a Subgroup and Proof that the Kernel is a Subgroup

We define what it means for H to be a subgroup of G and give clear criteria which you can follow in order to prove that a given subset is a subgroup. Then we prove that the kernel of f is a subgroup of G. I hope this helps someone learning abstract algebra. Useful Math Supplies https://am

From playlist Group Theory Problems

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Plenary lecture 2 by Emmanuel Breuillard - Part 1

Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma

From playlist Geometry Topology and Dynamics in Negative Curvature

Related pages

Subgroup series | Word (group theory) | Group theory