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akron1271041194.pdf (224.09 KB)
ETD Abstract Container
Abstract Header
Minimally Simple Groups and Burnside's Theorem
Author Info
Maurer, Kendall Nicole
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194
Abstract Details
Year and Degree
2010, Master of Science, University of Akron, Mathematics.
Abstract
William Burnside’s p
a
q
b
theorem is a very important result in group theory, which states that any group G of order p
a
q
b
is solvable. An interesting fact about this theorem is that it was originally proven using techniques from character theory, another branch of algebra. In fact, it was about seventy years before a group-theoretic proof of Burnside’s theorem was developed through the work of Goldschmidt, Matsuyama,Bender, and other mathematicians. Their approach to proving the theorem was to show that, in essence, minimally simple groups of size p
a
q
b
do not exist. Our purpose here is to use various techniques from the group-theoretic proof of Burnside’s theorem to establish and prove similar results about minimally simple groups G of arbitrary order.
Committee
James Cossey, Dr. (Advisor)
Jeffrey Riedl, PhD (Committee Member)
Antonio Quesada, PhD (Committee Member)
Pages
40 p.
Subject Headings
Mathematics
Keywords
minimally simple groups
;
simple groups
;
groups
;
group theory
;
Burnside
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Citations
Maurer, K. N. (2010).
Minimally Simple Groups and Burnside's Theorem
[Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194
APA Style (7th edition)
Maurer, Kendall.
Minimally Simple Groups and Burnside's Theorem.
2010. University of Akron, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194.
MLA Style (8th edition)
Maurer, Kendall. "Minimally Simple Groups and Burnside's Theorem." Master's thesis, University of Akron, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194
Chicago Manual of Style (17th edition)
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Document number:
akron1271041194
Download Count:
875
Copyright Info
© 2010, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.