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Dissertation Codegrees submitted.pdf (351.7 KB)
ETD Abstract Container
Abstract Header
p
-Group Codegree Sets and Nilpotence Class
Author Info
Croome, Sarah B
ORCID® Identifier
http://orcid.org/0000-0003-3940-8057
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456
Abstract Details
Year and Degree
2019, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
For a
p
-group
G
and an irreducible character χ of
G
, the codegree of χ is given by |
G
:ker(χ)|/χ(1). We investigate the relationship between the codegrees and nilpotence class of
p
-groups. If the set of codegrees of the irreducible characters of
G
has order 4, and
G
either has coclass at most 3, largest character degree
p
2
, or |
G
:
G'
|=
p
2
, then the nilpotence class of
G
is at most 4. Similar conditions exist which guarantee the existence of
p
2
as a codegree of
G
. If |
G
|=
p
n
then cod(
G
) contains all powers of
p
up to
p
n-1
if and only if
G
satisfies one of three cases in which
G
has maximal class or nilpotence class at most 2. We find families of maximal class groups which have consecutive
p
-power codegrees.
Committee
Mark Lewis (Advisor)
Stephen Gagola, Jr. (Committee Member)
Donald White (Committee Member)
Robert Walker (Committee Member)
Joanne Caniglia (Committee Member)
Pages
59 p.
Subject Headings
Mathematics
Keywords
groups
;
characters
;
codegrees
;
p-groups
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Croome, S. B. (2019).
p
-Group Codegree Sets and Nilpotence Class
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456
APA Style (7th edition)
Croome, Sarah.
p
-Group Codegree Sets and Nilpotence Class.
2019. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456.
MLA Style (8th edition)
Croome, Sarah. "
p
-Group Codegree Sets and Nilpotence Class." Doctoral dissertation, Kent State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456
Chicago Manual of Style (17th edition)
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Document number:
kent1554462855786456
Download Count:
338
Copyright Info
© 2019, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.