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Dissertation.pdf (1.98 MB)
ETD Abstract Container
Abstract Header
Character degree graphs of solvable groups
Author Info
Bissler, Mark W.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153
Abstract Details
Year and Degree
2017, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
We study character degree graphs of solvable groups. This is the graph whose vertex set consists of the primes dividing the character degrees of a group, and there is an edge between two vertices if there exists a character degree divisible by both primes. In particular, we investigate which graphs with six vertices can occur for any solvable group. We start with a total of one-hundred and twelve possible graphs and using known results, we are able to narrow the list of possible graphs down to twenty-seven. Next, by considering the twelve graphs that occur via direct product of groups we are able to reduce our list to fifteen graphs. We show six out of the remaining fifteen graphs cannot occur as the character degree graph of any solvable group. We note the remaining graphs with six vertices still under observation. Lastly, we use an inductive argument to show a specific family of graphs cannot occur as the character degree graph for any solvable group.
Committee
Mark Lewis (Advisor)
Pages
53 p.
Subject Headings
Mathematics
Keywords
character degree graph
;
degree graph
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Citations
Bissler, M. W. (2017).
Character degree graphs of solvable groups
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153
APA Style (7th edition)
Bissler, Mark.
Character degree graphs of solvable groups.
2017. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153.
MLA Style (8th edition)
Bissler, Mark. "Character degree graphs of solvable groups." Doctoral dissertation, Kent State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153
Chicago Manual of Style (17th edition)
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Document number:
kent1497368851849153
Download Count:
611
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.