Monthly Archives: March 2011

Groups having finitely many conjugacy classes of finite order elements

This post is based on a guest talk by Matt Clay. 1. How finite is this group? One way to measure how close a group is to being finite is by the finiteness property . Another way is to count … Continue reading

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Finiteness properties, Brown’s criterion and its application to Bieri-Stallings groups.

First we shall discuss an important result on finiteness properties of groups known as Brown’s Criterion. Then we shall use this result to prove the theorem discussed in our last post (and restated below) about finiteness properties of Bieri–Stallings groups. … Continue reading

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Morse Theory, finiteness properties, and Bieri–Stallings groups

In this post we shall discuss finiteness properties of groups and an important class of examples known as the Bieri–Stallings groups. Our main tool will be combinatorial Morse theory. Eilenberg–MacLane spaces and type In order to define our finiteness properties, … Continue reading

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VH-Complexes and subgroups of the direct product of two free groups

In this post we turn to Bridson and Wise‘s proof of the following theorem of Baumslag and Roseblade described in our previous post. Theorem. Every finitely presented subgroup of a direct product of two free groups is either free or … Continue reading

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Subgroups of the direct product of two free groups

Subgroups of the direct product of two finite rank free groups can be quite wild. In fact the direct product of two free groups contains very many subgroups, as per the following theorem of Baumslag and Roseblade. Theorem 1. There … Continue reading

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The Rips Construction, II

In the last post, we saw how Rips constructed a short exact sequence associated to any finitely presented group . was 2-generated and was small-cancellation ( for any desired ). In this post, we will see modifications due to Daniel … Continue reading

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