In the mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such that for consecutive subgroups X and Y in C, X is a normal subgroup of Y. The relation is written H ser G or H is serial in G. If the chain is finite between H and G, then H is a subnormal subgroup of G. Then every subnormal subgroup of G is serial. If the chain C is well-ordered and ascending, then H is an ascendant subgroup of G; if descending, then H is a descendant subgroup of G. If G is a locally finite group, then the set of all serial subgroups of G form a complete sublattice in the lattice of all normal subgroups of G. (Wikipedia).
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
Abstract Algebra | Normal Subgroups
We give the definition of a normal subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
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
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
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
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
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
Lecture 4: Equivariant CNNs I (Euclidean Spaces) - Maurice Weiler
Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slides: https://www.sci.unich.it/geodeep2022/slides/GroupEquivariantConvolutionalNetworksOnEuclideanSpaces.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Peter Scholze - Locally symmetric spaces, and Galois representations (4)
Lecture: Locally symmetric spaces, and Galois representations Speaker: Peter Scholze (The University of Bonn, Germany) Date: 25 Mar 2014, 11:30 AM Venue: AG 66, TIFR, Mumbai One of the most studied objects in mathematics is the modular curve, given as the locally symmetric space whic
From playlist Locally symmetric spaces, and Galois representations
Solving Hard Exams - Algebra and Arithmetic Exercise 2 - Ring Theory, Polynomials, Primes, Ideals
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.y
From playlist Solving Hard Exams!
Jean Bourgain - 1/2 The orbital circle method and applications...
Jean Bourgain - The orbital circle method and applications / Toral eigenfuctions and their nodal sets
From playlist École d'été 2014 - Théorie analytique des nombres
Ilya Shkredov: Zaremba’s conjecture and growth in groups
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 25, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Ergün Yalcin: Representation rings for fusion systems and dimension functions
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Measure Rigidity for forms of SL(2) by Manfred Einsiedler
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
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
CTNT 2022 - An Introduction to Galois Representations (Lecture 1) - by Alvaro Lozano-Robledo
This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)
Torsion units of integral group rings (Lecture 1) by Angel del Rio
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
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
Peter PATZT - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 1
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory