Toxic multinodular goitre can cause goitre (thyroid enlargement); within a goitre, nodules can develop. Risk factors for toxic multinodular goiter include individuals over 60 years of age and being female. Symptoms of toxic multinodular goitre are similar to that of hyperthyroidism, including: Sequence of events: Toxic multinodular goiter can be treated with antithyroid medications such as propylthiouracil or methimazole, radioactive iodine, or with surgery. Another treatment option is injection of ethanol into the nodules. The usage of terminology for types of goiter has varied over the past century. Physicians and surgeons tend to differentiate among solitary-nodule goiter, multinodular goiter, and non-nodular goiter more
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