Factorizations ofp-solvable groups

1-factorizations of Cayley graphs on solvable groups

A well known unresolved conjecture states that every Cayley graph on a solvable group G has a 1-factorization. We show that if the commutator subgroup of of such a group is an elementary abelian p-group, then every quartic Cayley graph on G has a 1-factorization.

Refined Factorizations of Solvable Potentials

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse and Coulomb potentials to obtain a wide set of raising and lowering operators, and to show clearly the connection that link these systems.

Characterization of Solvable Groups and Solvable radical

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.

Undistorted Solvable Linear Groups

We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.

Factorizations of Primitive Permutation Groups