Summer 2020 Projects 
Mailing addressREU programDept. of Math Sciences Kent State University Math & CS Building Summit Street, Kent OH 44242 ContactJenya Soprunovareu [at] math.kent.edu TEL: (330)6729086 FAX: (330) 6722209 
This year we will recruit nine students to work on the two projects described below. Ring Theory (Mikhail Chebotar)This Summer my group will be working on some problems related to the area of Ring Theory. Possible topics may include functional identities; radical theory; interactions between Ring Theory and Linear Algebra.
For the previous projects of my REU groups please visit https://sites.google.com/a/kent.edu/mikhailchebotar/reustude. Prerequisites: Linear Algebra (Theory of Matrices), Abstract Algebra. Graphs associated with groups (Mark Lewis)This is a project focused on finite groups. We will consider several graphs associated with groups to better understand the group. Using graphs to study groups has a long history going back to Cayley. The graphs that we are interested in have been introduced more recently. These graphs take as their vertices a subset of the elements of the group, and then there is an edge between two vertices if the subgroup generated by the two elements has certain properties. Two graphs that we will particularly focus on are the commuting graph and the cyclic graph. The commuting graph takes all noncentral elements of the group as it vertices and it put an edge between those elements if the two elements generate an abelian group. The cyclic graph takes all nonidentity elements as its vertices and puts an edge between two elements if they generate a cyclic group. We will work on determining the properties of these graphs for pgroups, nilpotent groups, and solvable groups. Prerequisites: At least one semester of undergraduate Abstract Algebra. References:
