Abstract Let G be a p -group for some prime . Recall that the Hughes subgroup of is generated by all elements with order not equal to In this paper, we prove if cyclic, then has exponent or cyclic dihedral. We also generalised quaternion, must quaternion. With these results in hand, classify tidy -groups.

Let α be an automorphism of the totally disconnected group G. The compact open subgroup, V , of G is tidy for α if [α(V ) : α(V ) ∩ V ] is minimised at V , where V ′ ranges over all compact open subgroups of G. Identifying a subgroup tidy for α is analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is developed here by showing that commut...

We study the P4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P4-domination in perfect graphs. This class strictly contains the P4-extendible graphs and the P4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P4-tidy graphs and P4-lite graphs are closely related. Note that the class of P4-lite graphs is a class of brittle graphs ...

We define the category of tidy symmetric multicategories. We construct for each tidy symmetric multicategory Q a cartesian monad (EQ, TQ) and extend this assignation to a functor. We exhibit a relationship between the slice construction on symmetric multicategories, and the ‘free operad’ monad construction on suitable monads. We use this to give an explicit description of the relationship betwe...

The tree-drawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an eecient algorithm for producing tidy drawings of trees. The speciication, the starting point for the derivations, consists of a collection of intuitively appealing criteria satissed by tidy drawings. The derivation shows constructively that these criteria completely ...

Let G be a totally disconnected, locally compact group and let H be a virtually flat (for example, polycyclic) group of automorphisms of G. We study the structure of, and relationships between, various subgroups of G defined by the dynamics of H. In particular, we consider the following four subgroups: the intersection of all tidy subgroups for H on G (in the case that H is flat); the intersect...