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THE STRUCTURE OF COMPOSITION

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0004
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the structure, as opposed to just the existence, of the family of homomorphisms among a set of graphs. The difference is noticeable with even just one graph. For instance, a ... More


TOWARDS 2 + 1 + 12 ·   3 ·   Aut   ( M 22 )

A. A. Ivanov

in The Fourth Janko Group

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198527596
eISBN:
9780191713163
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527596.003.0005
Subject:
Mathematics, Pure Mathematics

This chapter shows that N[3] is the extraspecial group Q[3] ≅ 21+12 + extended by a group R of order 3 acting fixed-point freely on Q[3]/Z[3] (where Z[3] is the centre of Q[3]/) and ... More


INTRODUCTION

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up ... More


Automorphisms of Free Groups

Matt Clay

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter discusses the automorphisms of free groups. Every group is the collection of symmetries of some object, namely, its Cayley graph. A symmetry of a group is called an automorphism; it is ... More


HOW TO CONTROL TYPES

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of ... More


The Dehn-Nielsen-Baer Theorem

Benson Farb and Dan Margalit

in A Primer on Mapping Class Groups (PMS-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter deals with the Dehn–Nielsen–Baer theorem, one of the most beautiful connections between topology and algebra in the mapping class group. It begins by defining the objects in the ... More


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