A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We investigate the case where H is the dihedral group. In many cases, G can be completely determined. In general, G can be proven to have many interesting properties. The theory is developed in terms of S-ring of Schur and Wielandt.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Nguyen, Long Pham Bao, "Fusion of Character Tables and Schur Rings of Dihedral Groups" (2008). All Theses and Dissertations. 1429.
group theory, S-rings, fusion, class algebra, character table