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DicksonC.the (final comments).pdf (159.6 KB)
ETD Abstract Container
Abstract Header
Conjugacy Class Sizes of the Symmetric and Alternating Groups
Author Info
Dickson, Cavan James
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=akron1396838435
Abstract Details
Year and Degree
2014, Master of Science, University of Akron, Mathematics.
Abstract
The symmetric group of degree n, denoted
S
n
, is the group of permutations on a set of cardinality n. The alternating group
A
n
is a subgroup of the symmetric group consisting of only the even permutations. In this thesis we study the sizes of the conjugacy classes of the symmetric and alternating groups, and the behavior of the zeta-type functions ζ
S
n
,A
n
(s) encoding these class sizes. In particular, we show that ζ
S
n
,A
n
(s)=1+Ο(n
-s
) , and deduce that ζ
S
n
,A
n
(s) → 0 as n → ∞. We also determine the conjugacy classes of relatively small and large sizes in these groups.
Committee
Hung Nguyen, Dr. (Advisor)
Stefan Forcey, Dr. (Committee Member)
Jeffrey Riedl, Dr. (Committee Member)
Pages
49 p.
Subject Headings
Mathematics
Keywords
symmetric group
;
alternating group
;
conjugacy class
;
largest
;
smallest
;
zeta function
;
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Refworks
EndNote
RIS
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Citations
Dickson, C. J. (2014).
Conjugacy Class Sizes of the Symmetric and Alternating Groups
[Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1396838435
APA Style (7th edition)
Dickson, Cavan.
Conjugacy Class Sizes of the Symmetric and Alternating Groups.
2014. University of Akron, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=akron1396838435.
MLA Style (8th edition)
Dickson, Cavan. "Conjugacy Class Sizes of the Symmetric and Alternating Groups." Master's thesis, University of Akron, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1396838435
Chicago Manual of Style (17th edition)
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Document number:
akron1396838435
Download Count:
317
Copyright Info
© 2014, some rights reserved.
Conjugacy Class Sizes of the Symmetric and Alternating Groups by Cavan James Dickson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Akron and OhioLINK.