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MATH 87100 Group Theory

Gilbert Baumslag's course at the Graduate Center, Fall 2008

Lecture 1 - contents

The list of topics that are likely to be discussed

Lecture 1

Topics discussed in the first lecture

Lecture 2

This is the second lecture in the course

Lecture 3 and an addendum for subgroups of free groups

This is now a reworking of Lecture 3. It describes how to generate a subgroup H of a group G with a given set of generators when one is also given a transversal of H in G. This leads one naturally to a proof of Schreier's theorem which asserts that subgroups of free groups are free. This proof was not given in class but is here described in detail. Some exercises will be provided in due course which show how this proof actually works in some concrete cases.

Lecture 4

The calculus of presentations and von Dyck's lemma

Exercises for period August 29 to October 17

Here are some exercises, mostly taken from Magnus, Karrass and Solitar

Lectures 6 and 7: Using presentations to describe groups

Presenting semi-direct products and defining free and amalgamated products via presentations.

Lecture 5

Basic groups, their presentations and group-theoretic constructions

Presenting semi-direct products

Here is a verification that the obvious way of presenting semi-direct products works

Problems to tst your skill

Try to figure out how to do the problems in the attached file and return to me after Thanksgiving.