1. Introduction and statement of results. "Let three points be specified on a line. Then one of the points is in the interior of the line segment joining the other two, and one of the points is exterior to the line segment joining the other two." This elementary statement concerning the ordering of three points on a line is capable of various extensions. Thus, e.g., it is easy to prove the foll...

In a finite projective plane π we consider two configuration conditions involving arcs in π and show via combinatorial means that they are equivalent. When the conditions hold we are able to obtain embeddability results for arcs, all proofs being elementary. In particular, when π = PG(2, q) with q even we provide short proofs of some well known embeddability results.

We show that it is possible to construct arbitrary order stable schemes for the homogeneous and heterogeneous wave equation in any dimension. The construction is elementary and uses formal power series techniques. We shall also calculate exact stability limits in various cases, and apparently this limit depends only on the dimension of the space.

A spanning subgraph F of a graph G is called a star-cycle factor of G ifeach component of F is a star or cycle. Let G be a graph and f : V (G) →{1, 2, 3, . . .} be a function. Let W = {v ∈ V (G) : f(v) = 1}. Under thisnotation, it was proved by Berge and Las Vergnas that G has a star-cyclefactor F with the property that (i) if a component D of F is a star withcenter v, t...

Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P , the subgroup Cl1(ZP ) of SK1(ZP ), in terms of a genetic basis of P . We also introduce a deflation map Cl1(ZP ) → Cl1 ( Z(P/N) ) , for a normal subgroup N of P , and show that it is always surjective. Along the way, we give a new ...

A simple upper bound on the size of nite subgroups of GL(n; Z) is given. Only elementary number-theoretic arguments are used, thereby avoiding previous methods depending on estimates of the Jordan number and the classiication of nite simple groups.

The present work aims to determine the solution f : R2 → R of the equation f(ux − vy, uy − vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) for all x, y, u, v ∈ R without any regularity assumption. The solution of the functional equation f(ux+ vy, uy− vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) is also determined. The methods of solution of these equations are simple and elementary. These two equations ...

F. Oger proved that if A is a nite group, then the class of groups which are abelian-by-A can be axiomatized by a single rst order sentence. It is established here that, in Oger's result, the word abelian cannot be replaced by group. In 2] it was proved that, if A is a nite group, then the class of groups G which have an abelian subgroup H such that G=H is isomorphic to A can be axiomatized by ...

In this paper we classify finite special Moufang sets M(U, τ ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author. We prove, using elementary means that U is elementary abelian. Then we show that M(U, τ ) is the unique Moufang set whose little projective group is PSL2(|U |). The emphasis of this paper is on obtaining elementary proofs. Secti...