Centre for the Mathematics of Symmetry and Computation

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Hua Zhang


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Hua Zhang

Thesis

Finite primitive groups with soluble stabilizers, with applications in graph theory

Summary

In this project we plan to study finite primitive permutation groups whose stabilizers are soluble, such primitive groups are of type affine, almost simple, and product action. For almost simple type, we present an explicit list of such groups and their soluble maximal subgroups. With this explicit list in hand, we are able to study (classify) some symmetric graphs, including edge- primitive s-arc transitive graphs with s>3, and 2-path transitive graphs which are not 2-arc transitive, and more.

Why my research is important

The study of finite primitive permutation groups with soluble stabilizers has a long history. Our research extends some of this earlier work, and it has been proved to be very useful.

Thanks to our research, some special families of symmetric graphs have been completely classified.


 

Centre for the Mathematics of Symmetry and Computation

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Last updated:
Tuesday, 1 November, 2011 2:52 PM

http://www.cmsc.uwa.edu.au/1880194