In this paper, we consider finite flag-transitive affine planes with a solvable automorphism group. Under a mild number-theoretic condition involving the order and dimension of the plane, the translation complement must contain a linear cyclic subgroup that either is transitive or has two equal-sized orbits on the line at infinity. We develop a new approach to the study of such planes by associ...

We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the np n+O(1) generator-enumeration algorithm. In previous work with Fabian Wagner, we showed an n logp n+O(logn/ log logn) time algorithm for testing isomorphism of p-groups by building graphs with degree bounded by p + O(1) that r...

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds (Kähler groups) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.

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

An algorithm for the construction of nite solvable groups of small order is given. A parallelized version under PVM is presented. Diierent models for parallelization are discussed. A nite group G is called solvable, if there exists a chain of normal subgroups