Iodine deficiency Iodine deficiency Iodine deficiency is a lack of the trace element iodine, an essential nutrient in the diet. It may result in a goiter, sometimes as an endemic goiter as well as cretinism due to untreated congenital hypothyroidism, which results in developmental delays and other health problems. Iodine deficiency is an important public health issue as it is a preventable cause of intellectual disability. Iodine is an essential dietary mineral; the thyroid hormones thyroxine and triiodothyronine contain iodine. In areas where there is little iodine in the diet, typically remote inland areas where no marine foods are eaten, iodine deficiency
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