Combinatorial Group Theory

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Classical Topology and Combinatorial Group Theory. John Stillwell. In recent years, many students have been introduced to topology in high school mathematics.

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Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams.

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Benjamin Fine , Anthony M. New Paperback Quantity Available: 1. Johnson wrote a book called Presentations of Groups". The proof of its security depends upon asymptotic group theory which we explain in Section 6. I mean - my supervisor read it when he was starting! The verifier checks to see if the evaluation of the sent word is correct or not. This involves what is called Nielsen transformations see [7] [8] [9].

In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book.

Apply filter. I would like to find examples of Complementing the red and blue boolean cube? Do we Is an HNN extension of a virtually torsion-free group virtually torsion-free? This is a cross post from Math. StackExchange after 2 weeks without an answer and a bounty being placed on the question.

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Sam Hughes 1 1 silver badge 10 10 bronze badges. Number of words of length N that reduce to the identity in a specific Coxeter group Suppose we have a Coxeter group whose diagram is given by a simplex. Craig 5 5 bronze badges.

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Many abstract Carl-Fredrik Nyberg Brodda 3 3 silver badges 10 10 bronze badges. Minimum Simple Burger-Mozes Type Group Burger and Mozes constructed Burger and Mozes - Lattices in products of trees infinite, finitely presented, torsion-free simple groups which split as amalgams of two finitely generated free groups Sebastien Palcoux 9, 4 4 gold badges 43 43 silver badges bronze badges.

AGenevois 2, 12 12 silver badges 25 25 bronze badges. Is there a name of semidirect product of a group with its automorphism group?

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In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used . Authors: Lyndon, Roger C., Schupp, Paul E. "This book () defines the boundaries of the subject now called combinatorial group theory. Lyndon, Roger C. (et al.).

Breakfastisready 12 12 bronze badges. I asked a very similar question here and got a wonderful answer. But now I need to change the question slightly this is the last question like this, I promise.

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Pat Devlin 1, 10 10 silver badges 15 15 bronze badges. When is the semidirect product of an elementary abelian group and a cyclic group generated by two elements?

Combinatorial Group Theory

I would be Is this YCC 1 1 gold badge 3 3 silver badges 10 10 bronze badges. Quotient groups of the lower central series of a surface group In the answer to MO question , it is possible to find a nice computation of the quotient groups of the lower central series of a finitely generated free group. What are the quotient Francesco Polizzi Can a hyperbolic, one ended, one relator group, have a shorter trivial word?

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It only takes a minute to sign up. I would please like some recommendations for an introductory level book on combinatorial group theory, by which I mean a group theory book which places emphasis on generators and relations and free groups, and then discusses common concepts such as quotient groups in terms of these.

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Thank you. This is an excellent introductory text. It is well written, covers a broad range of topics in geometric and combinatorial group theory, and contains lots of examples every second chapter is a study of an example. Also, it is modern - the other suggested texts are all 80s and earlier!

The other books are, of course, still very relevant, but Meier's book allows you to see where the subject is today, as opposed to in the pre-Gromov days.

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That said, I do not believe that you can survive in the world of combinatorial group theory without reading Magnus, Karrass and Solitar. So Meier's book is actually my secondary recommendation. Read Meier so that when you read Magnus, Karrass and Solitar you will understand it better. As mentioned, Presentations of Groups by D.

Johnson is nice. Topics in the Theory of Group Presentations by D.

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Combinatorial Group Theory by Roger C. Lyndon and Paul E.