There are strong analogies between groups definable in o-minimal structures and real Lie groups. Nevertheless, unlike the real case, not every definable group has maximal definably compact subgroups. We study definable groups G which are not definably compact showing that they have a unique maximal normal definable torsion-free subgroup N ; the quotient G/N always has maximal definably compact ...

iodine deficiency is the most important preventable cause of mental deficiency. the aim of this study was to specify the phase during fetal and postnatal development when iodine supplementation would have optimum effect on the prevention of brain damage. materials and methods forty schoolchildren aged 7-13 years, from the previously iodine deficient villages of kiga and randan, were divided int...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G of bounded index and G/G equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth auth...

A 1nite graph is said to be locally-quasiprimitive relative to a subgroup G of automorphisms if, for all vertices , the stabiliser in G of is quasiprimitive on the set of vertices adjacent to . (A permutation group is said to be quasiprimitive if all of its non-trivial normal subgroups are transitive.) The graph theoretic condition of local quasiprimitivity is strictly weaker than the condition...

It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their unive...

A finite transitive permutation group is said to be elusive if it has no fixed point free elements of prime order. In this paper we show that all elusive groups G = N oG1 with N an elementary abelian minimal normal subgroup and G1 cyclic, can be constructed from transitive subgroups of AGL(1, p2), for p a Mersenne prime, acting on the set of p(p + 1) lines of the affine plane AG(2, p).