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Character Tables Of Metacyclic Groups, Dane Christian Skabelund
Character Tables Of Metacyclic Groups, Dane Christian Skabelund
Theses and Dissertations
We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
Weak Cayley Table Isomorphisms, Long Pham Bao Nguyen
Weak Cayley Table Isomorphisms, Long Pham Bao Nguyen
Theses and Dissertations
We investigate weak Cayley table isomorphisms, a generalization of group isomorphisms. Suppose G and H are groups. A bijective map phi : G to H is a weak Cayley table isomorphism if it satisfies two conditions:(1) If x is conjugate to y, then phi(x) is conjugate to phi(y); (2) For all x, y in G, phi(xy) is conjugate to phi(x)phi(y).If there exists a weak Cayley table isomorphism between two groups, then we say that the two groups have the same weak Cayley table.This dissertation has two main goals. First, we wish to find sufficient conditions under which two groups have …
Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen
Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen
Theses and Dissertations
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 …