Low-dimensional topology | Geometric group theory

Subgroup distortion

In geometric group theory, a discipline of mathematics, subgroup distortion measures the extent to which an overgroup can reduce the complexity of a group's word problem. Like much of geometric group theory, the concept is due to Misha Gromov, who introduced it in 1993. Formally, let S generate group H, and let G be an overgroup for H generated by S ∪ T. Then each generating set defines a word metric on the corresponding group; the distortion of H in G is the asymptotic equivalence class of the function where BX(x, r) is the ball of radius r about center x in X and diam(S) is the diameter of S. Subgroups with constant distortion are called quasiconvex. (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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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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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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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

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Normal subgroups

Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a

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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Difference Between Normalizer, Centralizer, and Stabilizer

An easy way to remember what is the normalizer and centralizer of a subgroup, and what is the stabilizer of an element under a group action. For people learning abstract algebra! Group Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6 Subscribe to see

From playlist Group Theory

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GT2. Definition of Subgroup

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From playlist Abstract Algebra

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Hyperbolic groups, Cannon-Thurston maps, and hydra - Timothy Riley

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From playlist Mathematics

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Laurent Bartholdi - Imbeddings in groups of subexponential growth

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From playlist T1-2014 : Random walks and asymptopic geometry of groups.

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Algebraic Ending Laminations and Quasiconvexity by Mahan Mj

Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi

From playlist Surface Group Representations and Geometric Structures

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Thin Matrix Groups - a brief survey of some aspects - Peter Sarnak

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From playlist Mathematics

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Counting and dynamics in SL2 - Michael Magee

Michael Magee Member, School of Mathematics April 6, 2015 In this talk I'll discuss a lattice point count for a thin semigroup inside SL2(ℤ)SL2(Z). It is important for applications I'll describe that one can perform this count uniformly throughout congruence classes. The approach to count

From playlist Mathematics

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Gianluca Paolini: Torsion-free Abelian groups are Borel complete

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From playlist Logic and Foundations

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J. Wu: The Novikov conjecture and C*-algebras of infinite dimensional nonpositively curved spaces

Talk by Jianchao Wu in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 10, 2020.

From playlist Global Noncommutative Geometry Seminar (Americas)

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Plenary lecture 1 by Martin Bridson - Part 2

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From playlist Geometry Topology and Dynamics in Negative Curvature

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

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From playlist Group Theory Problems

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Group actions on 1-manifolds: A list of very concrete open questions – Andrés Navas – ICM2018

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From playlist Dynamical Systems and ODE

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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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Geometric group theory | Plaintext | Group representation | Baumslag–Solitar group | Lie group | Free abelian group | Locally finite group | Mathematics | Computable function | Rational number | Cryptosystem | Nilpotent group | Exponential growth | Normal subgroup | Word metric | Radius | Diameter