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Solvable Groups Whose Character Degree Graphs Have Diameter Three

Dugan, Carrie T.
http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573

Abstract Details

2007, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
In 2001 Lewis constructed a solvable group whose character degree graph has diameter three. In the construction of this group he used specific primes 2, 3, and 5. At the time it was known that the diameter of the degree graph of a solvable group must be at most three. Until then, however, no examples of solvable groups with diameter three degree graphs had materialized. It was even conjectured that no such group existed. My results expand on this original result by Lewis which left open the question as to whether or not more solvable groups exist with degree graphs of diameter three. Here we choose primes with certain divisibility conditions. The construction is the same as that of Lewis, which was a construction used by I.M. Isaacs. In general any primes can be used with this construction. However, the need arises for our restrictions on the primes so that the actions are coprime, and in some cases the actions are Frobenius. The result is that the character degree graphs for this family of groups is, in fact, isomorphic to the graph provided by Lewis.
Mark Lewis (Advisor)
Mathematics
Irr; ¿¿¿¿i; Lemma

Recommended Citations

Citations

  • Dugan, C. T. (2007). Solvable Groups Whose Character Degree Graphs Have Diameter Three [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573

    APA Style (7th edition)

  • Dugan, Carrie. Solvable Groups Whose Character Degree Graphs Have Diameter Three. 2007. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573.

    MLA Style (8th edition)

  • Dugan, Carrie. "Solvable Groups Whose Character Degree Graphs Have Diameter Three." Doctoral dissertation, Kent State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573

    Chicago Manual of Style (17th edition)

kent1185299573
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© 2007, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.