About Group Theory
A group is the collection of symmetries of an object. In the study of
group theory, there is an information exchange between a group and the
object on which the group acts. A modern approach comes from
considering the object to be the group itself, but as either a
geometric or a measure-theoretic object. The result is an interchange
between the algebraic information of a group and its geometric and
measure-theoretic counterparts. The class of finitely generated groups
provides a rich and natural source of examples for this framework,
yielding an expansive field of research that touches upon many
beautiful areas of mathematics.
