Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
Dissertation.pdf (413.63 KB)
ETD Abstract Container
Abstract Header
INDUCED CHARACTERS WITH EQUAL DEGREE CONSTITUENTS
Author Info
Lyons, Corey Francis
ORCID® Identifier
http://orcid.org/0000-0002-4773-9908
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1461594819
Abstract Details
Year and Degree
2016, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
We investigate the situation where each of the nonprincipal irreducible characters of a subgroup
H
of a finite group
G
, induce to
G
as a sum of irreducible characters, all of equal degree. When this situation occurs, either
H
is contained in
G'
or
G'
is contained in
H
. When the normal closure of
H
in
G
is proper in
G'
, then the normal closure of
H
in
G
is solvable, although
G
need not be solvable. We show that
G
is solvable when
H
is proper in
G'
and the normal closure of
H
in
G
is equal to
G'
. It has been conjectured that
H
is subnormal in
G
. We present a partial result and a related family of examples.
Committee
Stephen Gagola, Jr./Dr. (Advisor)
Pages
33 p.
Subject Headings
Mathematics
Keywords
group theory
;
character theory
;
character degrees
;
induced characters
;
solvable
;
subnormal
;
equal degree constituents
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Lyons, C. F. (2016).
INDUCED CHARACTERS WITH EQUAL DEGREE CONSTITUENTS
[Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1461594819
APA Style (7th edition)
Lyons, Corey.
INDUCED CHARACTERS WITH EQUAL DEGREE CONSTITUENTS.
2016. Kent State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1461594819.
MLA Style (8th edition)
Lyons, Corey. "INDUCED CHARACTERS WITH EQUAL DEGREE CONSTITUENTS." Doctoral dissertation, Kent State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1461594819
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
kent1461594819
Download Count:
757
Copyright Info
© 2016, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.