Goitre a choker, dubbed "Kropfband" (struma band) which was used to hide either the goitre or the remnants of goitre surgery. In the 1920s wearing bottles of iodine around the neck was believed to prevent goitre. The coat of arms and crest of Die Kröpfner, of Tyrol showed a man "afflicted with a large goitre", an apparent pun on the German for the word ("Kropf"). Goitre A goitre, or goiter, is a swelling in the neck resulting from an enlarged thyroid gland. A goitre is associated with a thyroid that is not functioning properly. Worldwide, over 90% of goitre cases are
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