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Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces
Whitaker, erica j.

2011, Doctor of Philosophy, Ohio State University, Mathematics.
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.
James Cogdell, PhD (Advisor)
Warren Sinnott, PhD (Committee Member)
Thomas Kerler, PhD (Committee Member)
112 p.

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Whitaker, e. (2011). Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Whitaker, erica. "Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces." Electronic Thesis or Dissertation. Ohio State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Whitaker, erica "Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces." Electronic Thesis or Dissertation. Ohio State University, 2011. https://etd.ohiolink.edu/

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