Algebra Seminar talk
Almost free groups of an unusual sort
Almost free groups (groups whose subgroups of smaller cardinality are free) have furnished a plentitude of curious examples for 60 years. Some such groups can be made to satisfy further conditions which are satisfied by free groups, while still failing to be free. Principles of combinatorial set theory generally play a role in such constructions. I’ll give a review of almost free groups, including history and some examples, and present a very recent result.