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osu1321205804.pdf (953.81 KB)
ETD Abstract Container
Abstract Header
Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces
Author Info
Whitaker, erica j.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1321205804
Abstract Details
Year and Degree
2011, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
There is an established bijection between finite-index subgroups Γ of Γ(2) and bipartite graphs on surfaces, or, equivalently, triples of permutations. We utilize this relationship to study noncongruence subgroups in terms of the corresponding graphs. In particular, we will produce infinite families of noncongruence subgroups of Γ(2) of every even level by constructing their associated graphs. Also, given a graph on a surface, we have a method to produce generators for the corresponding group Γ in terms of the generators of Γ(2). Given generators for Γ(2n), we show how to determine whether or not a graph of level 2n corresponds to a congruence subgroup. Finally we give an algorithm to find permutations and generators for groups of the form Γ(2p) for p prime.
Committee
James Cogdell, PhD (Advisor)
Warren Sinnott, PhD (Committee Member)
Thomas Kerler, PhD (Committee Member)
Pages
112 p.
Subject Headings
Mathematics
Keywords
graphs on surfaces
;
congruence subgropus
;
noncongruence subgroups
;
modular group
;
tilings
;
permutations
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Citations
Whitaker, E. J. (2011).
Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1321205804
APA Style (7th edition)
Whitaker, erica.
Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces.
2011. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1321205804.
MLA Style (8th edition)
Whitaker, erica. "Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1321205804
Chicago Manual of Style (17th edition)
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Document number:
osu1321205804
Download Count:
866
Copyright Info
© 2011, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.