# Absolute presentation of a group

In mathematics, an absolute presentation is one method of defining a group. Recall that to define a group by means of a presentation, one specifies a set of generators so that every element of the group can be written as a product of some of these generators, and a set of relations among those generators. In symbols: Informally is the group generated by the set such that for all . But here there is a tacit assumption that is the "freest" such group as clearly the relations are satisfied in any homomorphic image of . One way of being able to eliminate this tacit assumption is by specifying that certain words in should not be equal to That is we specify a set , called the set of irrelations, such that for all (Wikipedia).

Visual Group Theory, Lecture 1.4: Group presentations

Visual Group Theory, Lecture 1.4: Group presentations We begin this lecture by learning how to take a Cayley diagram and label its nodes with the elements of a group. Such a labeled diagram can function as a "group calculator". It leads to the notion of a "group presentation", which is a

From playlist Visual Group Theory

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From playlist Abstract algebra

Visual Group Theory, Lecture 1.6: The formal definition of a group

Visual Group Theory, Lecture 1.6: The formal definition of a group At last, after five lectures of building up our intuition of groups and numerous examples, we are ready to present the formal definition of a group. We conclude by proving several basic properties that are not built into t

From playlist Visual Group Theory

Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory

Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in u

From playlist Essence of Group Theory

What is a Group? | Abstract Algebra

Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s

From playlist Abstract Algebra

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The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin

From playlist Abstract Algebra

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From playlist Modern Algebra - Chapter 15 (groups)

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From playlist Group theory

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From playlist Mathematical Physics

CTNT 2020 - G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range - Jeremy Booher

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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From playlist Algebraic and Complex Geometry

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From playlist Group Theory and Computational Methods

VassarStats - Clinical Block 2 Example

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From playlist Group Algebras, Representations And Computation

Representations of pp-adic groups - Jessica Fintzen

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From playlist Mathematics

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From playlist Group Theory and Computational Methods

Modulo p Representations of GL_2 (K) (Lecture 2) by Benjamin Schraen

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Endomorphisms of certain superelliptic jacobians and l-adic (..) - Zarhin - Workshop 2 - CEB T2 2019

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From playlist 2019 - T2 - Reinventing rational points

Visual Group Theory, Lecture 3.4: Direct products

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From playlist Visual Group Theory