Feb 27, 2011 ... Motivation Very often in group theory we are dealt groups which, to our… ... In
essence the commutator subgroup is precisely such that when the ambient ....
Pingback by University of Maryland College Park Qualifying Exams ...

Commutator (group theory)

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.

This is an excerpt from the article Commutator (group theory) from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

This is an excerpt from the article Commutator (group theory) from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

The article Commutator (group theory) at en.wikipedia.org was accessed 14 times in the last 30 days. (as of: 05/23/2014)

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Commutator - Wikipedia, the free encyclopedia

[edit]. The commutator of two elements, g and h, of a group G, is the element. [g, h
] = g−1h−1gh. It is equal to the group's identity if ...

en.wikipedia.org/wiki/Commutator

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Commutator subgroup - Wikipedia, the free encyclopedia

The commutator subgroup is important because it is the smallest normal
subgroup such that the quotient group of the original group by this ... 2.1 Derived
series; 2.2 Abelianization; 2.3 Classes of groups .... Group theory · Functional
subgroups.

en.wikipedia.org/wiki/Commutator_subgroup

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Commutator -- from Wolfram MathWorld

There is a related notion of commutator in the theory of groups. The commutator
of two group elements A and B is ABA^(-1)B^(-1) , and two elements A and B ...

mathworld.wolfram.com/Commutator.html

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Commutator (group theory) - The Free Dictionary

com·mu·ta·tor (k m y -t t r). n. 1. A cylindrical arrangement of insulated metal bars
connected to the coils of a direct-current electric motor or generator, providing a ...

www.thefreedictionary.com/Commutator+(group+theory)

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group theory - Let $C$ be the commutator subgroup of $G$. Prove ...

Nov 30, 2011 ... This can be done for any elements, so $G/C$ is abelian. This seems somewhat
surprisingly short. Is that all there is to it? Regards. group-theory ...

math.stackexchange.com/questions/87082/

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Commutator Subgroup - Group Theory - MathOverflow

Jul 9, 2012 ... The commutator subgroup of the free group $\langle a,b \rangle$ is freely
generated by the set $$\lbrace [a^n,b^m] \mid n,m \in \mathbb Z, nm ...

mathoverflow.net/questions/101746/commutator-subgroup-group-theory

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gr.group theory - Commutator subgroup does not consist only of ...

Oct 30, 2010 ... The problem is whether the commutator subgroup may contain elements that are
not commutators. One example are the free groups.

mathoverflow.net/questions/44269/

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gr.group theory - Non-commutator in simple group? - MathOverflow

May 1, 2012 ... For a group $G$, we say that $x\in G$ is a commutator if there exists $a,b \in G$
such that $x=a^{1}b^{-1}ab$, and we say that $x$ is a ...

mathoverflow.net/questions/95692/non-commutator-in-simple-group

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On commutators in groups - University of Evansville

characters of nonabelian groups. They are now an established and immensely
useful tool in all of group theory. Commutators became objects of interest in their
...

faculty.evansville.edu/rm43/publications/commutatorsurvey.pdf

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COMMUTATOR THEORY FOR LOOPS 1 ... - Math Department

sults summarized in Corollary 5.2. Generating sets in terms of elementwise
associators and commutators, a traditional approach of group theory and loop
theory, ...

web.cs.du.edu/~petr/data/papers/commutator_theory_for_loops.pdf

Search results for "Commutator (group theory)"

Google: approx. 169.000

Commutator (group theory) in science

Review of Group Theory: The Commutator Subgroup and - Abstract ...

[PDF]On commutators in groups - University of Evansville

characters of nonabelian groups. They are now an established and immensely
useful tool in all of group theory. Commutators became objects of interest in their
...

[PDF]GROUP THEORY NOTES FOR THE COURSE ... - McGill University

MCGILL UNIVERSITY, FALL 2003, ... Commutator subgroup ... at least in the theory of finite groups on which this course focuses, there is no comparable theory ...

[PDF]Commutator Theory for Loops

joint work with Petr Vojtechovský, University of Denver ... Commutators for loops.
1 / 11 ... Bruck's approach (1950's), by direct analogy to group theory:.

University of Isfahan International Journal of Group Theory 2251 ...

University of Isfahan International Journal of Group Theory 2251-7650 3 1 2014 ... (soluble-by-finite) group whose proper subgroups have minimax commutator ...

Commutator - Wikipedia, the free encyclopedia

1 Group theory. 1.1 Identities. 2 Ring theory. 2.1 Identities. 3 Graded rings and
algebras; 4 Derivations; 5 Anticommutator; 6 See also; 7 Notes; 8 References ...

[PDF]Commutator Theory for Loops

Commutator Theory for Loops. David Stanovský. Charles University, Prague,
Czech Republic stanovsk@karlin.mff.cuni.cz joint work with Petr Vojtechovský, ...

Stable commutator length on mapping class groups

Jun 11, 2013 ... Mathematics > Group Theory ... the Nielsen-Thurston decomposition) when an
element $g\in\Gamma$ has positive stable commutator length.

Books on the term Commutator (group theory)

Commutator Calculus and Groups of Homotopy Classes

PART A: HOMOTOPY OPERATIONS, NILPOTENT GROUP THEffl AND
NILPOTENT LIE ALGEBRA THEORY L COMMUTATOR CALCULUS Commutator
calculus is a branch of group theory dealing with nilpotent groups, Lie algebras,
the ...

C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians (Progress in Mathematics)

The conjugate operator method is a powerful recently develop- ed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially optimal results in situations as varied as ordinary differential operators, pseudo-differenti...

Commutator Calculus and Groups of Homotopy Classes (London Mathematical Society Lecture Note Series)

The author extends results of rational homotopy theory to a subring of rationals; the methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic study of the algebraic properties of the classical homotopy operations. -- Book Deacription

Group Theory: An Intuitive Approach

What is the commutator subgroup of the quaternion group (pb. III.2.e-4, p. 74)?
Find the commutator subgroups of the geometric groups, and discuss the
reasons, group theoretical and particularly geometrical, for elements being commutators, ...

Mathematical Physics: A Modern Introduction to Its Foundations

PAGEOPH [Pure and Applied Geophysics] Review by Daniel Wojcik, University of Maryland "This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interlud...

Combinatorial Group Theory, Discrete Groups, and Number ...

Introduction This paper addresses some questions concerning the commutator
calculus - an important area of Combinatorial Group Theory. We first recall some
basic definitions and terminology. Suppose G is a group. Let a,b £ G. Then the ...

Fundamentals of Group Theory: An Advanced Approach

Nontrivial groups with no nontrivial proper normal subgroups are, in some sense,
simple. ... note that authors who define the conjugate of 84 Fundamentals of Group Theory Simple Groups Commutators of Elements Commutators of
Elements.

Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60)

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of...

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Online sources for the term

Commutator (group theory)

Commutator (group theory)

Hazewinkel, Michiel, ed. (2001), "Commutator", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

www.encyclopediaofmath.org/index.php?title=p/c023430
Blog posts on the term

Commutator (group theory)

Commutator (group theory)

You can solve the cube – with commutators! | Geometry and the imagination

You can solve the cube – with commutators!
August 24, 2013 in Groups | Tags: commutators, group theory, Rubik's cube
After a couple years of living out of suitcases, we recently sold our house in Pasadena, and bought a new one in Hyde Park. All our junk was shipped to us, and the boxes we didn’t feel like unpacking are all sitting around in the attic, where the kids have been spending a lot of time this summer.

lamington.wordpress.com/2013/08/24/you-can-solve-the-cube-with-commutators/
Review of Group Theory: The Commutator Subgroup and the Abelianization of a Group « Abstract Nonsense

Point of post: In this post we discuss the notion of the commutator subgroup of a group $latex G$ and prove some basic, yet important, facts about it. We then discuss the abelianization of a group (the group mod the commutator subgroup). Motivation Very often in group theory we are dealt groups which, to our…

drexel28.wordpress.com/2011/02/27/review-of-group-theory-the-commutator-subgroup-and-the-abelianization-of-a-group/
Operator Algebra II – The Commutator | Mathematics in Chemical Theory

Anybody who has taken an undergraduate course on quantum chemistry or quantum mechanics is familiar with the commutator on some level. In these courses, I was told how to use it to carry out some basic (but very important!) calculations, and was given a teaser of its physical significance in terms of incompatible observables. In…

chemicalmathematics.wordpress.com/2013/02/06/operator-algebra-ii-the-commutator/
Perfect groups of infinite commutator length: setup | On music, computing and math

At the end of my post Some trivia on derived subgroups I quickly mention that what I had been discussing up to then is essentially about the commutator length of the group. Recall that the derived subgroup is the group generated by all commutators, and that a group is said to be perfect if and only…

pbelmans.wordpress.com/2012/09/11/perfect-groups-of-infinite-commutator-length-setup/
Conjugacy class of commutators of generators for a free group. | | Free EducationFree Education

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Let $F$ be a free group generated by two elements. Let $\{a,b\}$ and $\{c,d\}$ are two different generating set.

3mr.me/conjugacy-class-of-commutators-of-generators-for-a-free-group/
quantum field theory - Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group - Physics Stack Exchange
physics.stackexchange.com/questions/38573/calculating-the-commutator-of-pauli-lubanski-operator-and-generators-of-lorentz

(Collective) Introduction to Commutators

This is more experimental than most threads, and I've been hoping to do a collective tutorial at some point.
Let's talk about Comms.
How would we go about teaching this very very important subject to noobs, with everything they could need to know?
There have been a few tutorials floating about over the years, and quite a few explanations. I think there needs to finally be a "from noob to optimizer" walkthrough of sorts that can finally bridge this gap.
I won't even contribute right

www.speedsolving.com/forum/showthread.php?32626-(Collective)-Introduction-to-Commutators
Commutator Subgroups « The Unapologetic Mathematician

If we have a group $latex G$, it may or may not be abelian. We can measure how nonabelian it is with the commutator subgroup $latex \left[G,G\right]$. This is the subgroup generated by all the commutators in $latex G$. Start with all the elements of $latex G$ of the form $latex ghg^{-1}h^{-1}$ with $latex g$…

unapologetic.wordpress.com/2007/03/14/commutator-subgroups/
Nationals 2010 | Annoying Precision

MIT is hosting the United States Rubik's Cube Championships this summer, August 6-8. All ages welcome! Normally I wouldn't post about such things, but I happen to be a member of the Rubik's Cube club here, and Some people use the Rubik's cube group to motivate group theory. I'm a fan of hands-on mathematics, and…

qchu.wordpress.com/2010/04/12/nationals-2010/
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