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Character Degree Graphs of Solvable ...

ProQuest Information and Learning Co.

Character Degree Graphs of Solvable Groups.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Character Degree Graphs of Solvable Groups./
作者:	Bissler, Mark William.
面頁冊數:	1 online resource (53 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369980059

Character Degree Graphs of Solvable Groups.
Bissler, Mark William.

Character Degree Graphs of Solvable Groups. - 1 online resource (53 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369980059Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Character Degree Graphs of Solvable Groups.
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100 1 $a Bissler, Mark William. $3 1180913
245 1 0 $a Character Degree Graphs of Solvable Groups.
264 0 $c 2017
300 $a 1 online resource (53 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Mark Lewis.
502 $a Thesis (Ph.D.) $c Kent State University $d 2017.
504 $a Includes bibliographical references
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Kent State University. $b Mathematical Science. $3 1180914
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10626772 $z click for full text (PQDT)

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