Event Type:

Graduate Student Summer Seminar

Date/Time:

Monday, July 10, 2017 - 14:30 to 15:30

Location:

Kidder 364

Abstract:

A group described in terms of a group presentation

can be difficult to understand. In general, even determining

if such a group is trivial is not algorithmically decidable.

However, it is easy to define group homomorphisms whose domain

has a known presentation, and these homomorphisms can be used

to study the domain and its elements. In this talk, we investigate

a property of groups called residual finiteness, which guarantees

the existence of especially useful homomorphisms. We give examples

of presentations which define groups that are or are not residually

finite. We then explore characterizations of residual finiteness,

stronger and weaker conditions, and methods of constructing new

residually finite groups from old.