Iodine in biology damage). In areas where there is little iodine in the diet, typically remote inland areas and semi-arid equatorial climates where no marine foods are eaten, iodine deficiency also gives rise to hypothyroidism, the most serious symptoms of which are epidemic goitre (swelling of the thyroid gland), extreme fatigue, mental slowing, depression, weight gain, and low basal body temperatures. The addition of iodine to table salt (so-called iodized salt) has largely eliminated the most severe consequences of iodine deficiency in wealthier nations, but deficiency remains a serious public health problem in the developing world. Iodine deficiency is also a problem in
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