A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Dexter, Cache Porter, "Schur Rings over Infinite Groups" (2019). Theses and Dissertations. 8831.
Schur ring, permutation group, free group, free abelian group, infinite cyclic group