Sorin Popa initiated the study of Polish groups which are embeddable into the
unitary group of a separable finite von Neumann algebra. Such groups are called
of finite type. We give necessary and sufficient conditions for Polish groups
to be of finite type, and construct exmaples of such groups from semifinite von
Neumann algebras. We also discuss permanence properties of finite type groups
under various algebraic operations. Finally we close the paper with some
questions concerning Polish groups of finite type.Comment: 20 page
