Celebratio Mathematica — Jones

Complete Bibliography

Works connected to Marston Donald Edward Conder

Filter the Bibliography List

year	title	people

			clear

M. Conder and V. Jones: “Highly transitive imprimitivities,” J. Algebra 300 : 1 (2006), pp. 44–56. MR 2228633 Zbl 1111.20001 article

Some new observations are made about imprimitive permutation groups associated with subfactors of von Neuman algebras. Of particular interest are examples of a group \( G \) containing two maximal subgroups \( H \) and \( K \) such that \( G\neq HK \), and such that the action of \( G \) on the space of cosets of \( H\cap K \) has small rank (few suborbits). The rank 6 case turns out to correspond to the action of the collineation group on flags of a Desarguesian projective plane, and a special case of interest for rank 7 corresponds to the action of a 4-transitive group on ordered pairs of distinct points. Some other new (and unexpected) fundamental properties of groups are described along the way.