The negative charge of this kind of supramolecular assembly is suitable for counter anions in conductive cation radical salts. Not only can it accomplish charge balance in the salt, it can also restrict the packing mode of the donor molecules (= cation radical molecules ∗1 ) which governs the physical properties of the salt. Compared to discrete anions, such as I3 or ClO4 , used in most other c...

We report the synthesis of a series of homologous oligoviologens in which different numbers of 4,4'-bipyridinium (BIPY(2+)) subunits are linked by p-xylylene bridges, as a prelude to investigating how their radical cationic forms self-assemble both in solution and in the solid state. The strong radical-radical interactions between the radical cationic forms of the BIPY(2+) units-namely, BIPY(•+...

We establish a correspondence between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive characteristic, then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be to...

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost maximally almost-periodic group topology. Some open problems are also formulated.

We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x ∈ G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite dimensional Lie algebras and some classes of infinite groups. To Charles Leedham-Green on his 65th birthday

We establish a link between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive characteristic , then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be torsion fre...

We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.

Let α be an infinite cardinal. In this paper we define an interpolation rule IR(α) for lattice ordered groups. We denote by C(α) the class of all lattice ordered groups satisfying IR(α), and prove that C(α) is a radical class.