Department of Mathematics
Server

This is a summary of the work done during a summer undergraduate research project by Mercedes Scott under my direction.

A careful literature search yielded more results than I had been aware of, including a complete characterization of which finite groups G of odd order can be the group of units of a ring R, together with a characterization of the subring of R generated by G. The proofs use some standard, but advanced, ideas from ring theory. One will be outlined in this talk.

Nonetheless, we had completely elementary proofs of the fact that certain finite groups could not be the group of units of a ring; and we searched hard for an elementary proof of the (known to be true) statement that Z/(6k+5) is not the group of units of a ring for any k. Ultimately this search was unsuccessful, but we observed many interesting patterns along the way, and involved two other members of the department (Drs Gunderson and Craigen) in the project before the end.