Ben Fairbairn
My main interests lie in Group Theory. More specifically I am mainly interested in Finite Simple Groups and in Reflection Groups along with combinatorial and geometrical structures related to them such as Graphs, Designs and Representations. I have also become interested in using the actions of groups on curves to define surfaces with interesting geometric properties.
Supervisors: Professor Robert Turner Curtis
Address: Department of Economics, Mathematics and Statistics,
Birkbeck, University of London
Malet Street,
London,
WC1E 7HX
Supervisors: Professor Robert Turner Curtis
Address: Department of Economics, Mathematics and Statistics,
Birkbeck, University of London
Malet Street,
London,
WC1E 7HX
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real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We will also discuss the case of characteristically simple groups and almost simple groups. En route we shall discuss several questions, open problems and conjectures as well as giving several new examples of infinite families of strongly real Beauville groups.
and Gonzalez-Diez. In doing so we complete the classication of alternating groups that possess strongly real Beauville structures. We conclude by discussing mixed Beauville structures of the
groups A6 : 2 and A6:2^2.
automorphism group of the lattice. For the tetrad A he denoted this automorphism \zeta_A. It is well known that for \zeta_A and \zeta_B to commute is sufficient to have A and B belong to the same sextet. We extend this to a necessary and sufficient condition, namely \zeta_A and \zeta_B will commute if and only if A\cup B is contained in a block of S. We go on extend this result to similar conditions for other elements of the group and show how neatly these results restrict to certain subgroups.
standard presentations of the finite simply laced irreducible finite
Coxeter groups, that is the Coxeter groups of types An, Dn and
En and show that these are naturally arrived at purely through
consideration of certain natural actions of symmetric groups. We
go on to use these techniques to provide explicit representations of these groups.
real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We will also discuss the case of characteristically simple groups and almost simple groups. En route we shall discuss several questions, open problems and conjectures as well as giving several new examples of infinite families of strongly real Beauville groups.
and Gonzalez-Diez. In doing so we complete the classication of alternating groups that possess strongly real Beauville structures. We conclude by discussing mixed Beauville structures of the
groups A6 : 2 and A6:2^2.
automorphism group of the lattice. For the tetrad A he denoted this automorphism \zeta_A. It is well known that for \zeta_A and \zeta_B to commute is sufficient to have A and B belong to the same sextet. We extend this to a necessary and sufficient condition, namely \zeta_A and \zeta_B will commute if and only if A\cup B is contained in a block of S. We go on extend this result to similar conditions for other elements of the group and show how neatly these results restrict to certain subgroups.
standard presentations of the finite simply laced irreducible finite
Coxeter groups, that is the Coxeter groups of types An, Dn and
En and show that these are naturally arrived at purely through
consideration of certain natural actions of symmetric groups. We
go on to use these techniques to provide explicit representations of these groups.
together elements of the Conway group dotto represented in a very succinct fashion thereby making this extremely succinct representation practical to use.