The residually weakly primitive geometries of S5×2

The Residually Weakly Primitive Geometries of M22

In [6], Dehon and the author described two algorithms to classify all geometries Γ of a given group G such that Γ is a firm and residually connected geometry and G acts flag-transitively and residually weakly primitively on Γ. We stated in that paper that these programs were able to classify all geometries with Borel subgroup not equal to the identity of G when G is the Hall-Janko group J2. In ...

The residually weakly primitive geometries of HS

The Residually Weakly Primitive Geometries of J 3

Rank Three Residually Connected Geometries for M22, Revisited

The rank 3 residually connected flag transitive geometries Γ for M22 for which the stabilizer of each object in Γ is a maximal subgroup of M22 are determined. As a result this deals with the infelicities in Theorem 3 of Kilic and Rowley, On rank 2 and rank 3 residually connected geometries for M22. Note di Matematica, 22(2003), 107–154.

Profinite Groups Associated with Weakly Primitive Substitutions

A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword which is a factor of all its infinite factors, that is one which lies in a J -class with only finite words strictly J -above it. Such a J -class is regular and therefore it has an associated...