Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.633408
Title: Finite groups of small genus
Author: Mohammed Salih, Haval M.
ISNI:       0000 0004 5366 5452
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2015
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Abstract:
For a finite group $$G$$, the Hurwitz space $$H$$$$^i$$$$_r$$$$_,$$$$^n$$$$_g$$ ($$G$$) is the space of genus $$g$$ covers of the Riemann sphere with $$r$$ branch points and the monodromy group $$G$$. Let ε$$_r$$($$G$$) = {($$x$$$$_1$$,...,$$x$$$$_r$$) : $$G$$ = $$\langle$$$$x$$$$_1$$,...,$$x$$$$_r$$$$\rangle$$, Π$$^r$$$$_i$$$$_=$$$$_1$$ $$x$$$$_i$$ = 1, $$x$$$$_i$$ ϵ $$G$$#, $$i$$ = 1,...,$$r$$}. The connected components of $$H$$$$^i$$$$_r$$$$_,$$$$^n$$$$_g$$($$G$$) are in bijection with braid orbits on ε$$_r$$($$G$$). In this thesis we enumerate the connected components of $$H$$$$^i$$$$_r$$$$_,$$$$^n$$$$_g$$($$G$$) in the cases where $$g$$ $$\leq$$ 2 and $$G$$ is a primitive affine group. Our approach uses a combination of theoretical and computational tools. To handle the most computationally challenging cases we develop a new algorithm which we call the Projection-Fiber algorithm.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.633408  DOI: Not available
Keywords: QA Mathematics
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