a1 California Institute of Technology, Pasadena, California 91125, USA (email: firstname.lastname@example.org)
We give a qualitative description of the set G(H) of overgroups in G of primitive subgroups H of finite alternating and symmetric groups G, and particularly of the maximal overgroups. We then show that certain weak restrictions on the lattice G(H) impose strong restrictions on H and its overgroup lattice.
(Received September 01 2007)
(Accepted June 06 2008)
2000 Mathematics subject classification
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This work was partially supported by grant no. NSF-0504852.