Congenital iodine deficiency syndrome degree of iodine deficiency was milder and manifested primarily as thyroid enlargement rather than severe mental and physical impairment. In Switzerland, for example, where soil does not contain a large amount of iodine, cases of congenital iodine deficiency syndrome were very abundant and even considered genetically caused. As the variety of food sources dramatically increased in Europe and North America and the populations became less completely dependent on locally grown food, the prevalence of endemic goitre diminished. The early 20th century saw the discovery of the relationships of neurological impairment with hypothyroidism due to iodine deficiency. Both have been largely
Trace field of a representation of formula_4 (see for example in ). The "invariant trace field" is equal to the trace field of the subgroup formula_7 generated by all squares of elements of formula_4 (a finite-index subgroup of formula_4). The invariant trace field of Fuchsian groups is stable under taking commensurable groups. This is not the case for the trace field; in particular the trace field is in general different from the invariant trace field. Let formula_4 be a Fuchsian group and formula_11 its trace field. Let formula_12 be the formula_11-subalgebra of the matrix algebra formula_14 generated by the preimages of elements of formula_4. The