Giovanni Falcone

Algebraic groups and Lie groups with few factors

Prerequisites.- Extensions.- Groups of Extreme Nilpotency Class.- Chains.- Groups with Few Types of Isogenous Factors.- Three-Dimensional Affine Groups.- Normality of Subgroups.

Monothetic algebraic groups

We call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.

Multiplicative loops of 2-dimensional topological quasifields

We determine the algebraic structure of the multiplicative loops for locally compact 2-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a 1-dimensional compact subgroup. In the last section, we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension 4 admitting an at least 7-dimensional Lie group as collineation group.

On 2 – (n2, 2n, 2n–1) designs with three intersection numbers

The simple incidence structure

Witt vectors and Fermat quotients

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Kirkman's tetrahedron and the fifteen schoolgirl problem

, formed by the points and the unordered pairs of distinct parallel lines of a finite affine plane

Algebraic Frobenius groups

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