Goitre an underactive thyroid, thyroid supplements are used as treatment. Sometimes a partial or complete thyroidectomy is required. Goitre is more common among women, but this includes the many types of goitre caused by autoimmune problems, and not only those caused by simple lack of iodine. Chinese physicians of the Tang Dynasty (618–907) were the first to successfully treat patients with goitre by using the iodine-rich thyroid gland of animals such as sheep and pigs—in raw, pill, or powdered form. This was outlined in Zhen Quan's (d. 643 AD) book, as well as several others. One Chinese book, "The Pharmacopoeia of
Trace field of a representation that for Fuchsian groups. One big difference is that the trace field of a group of finite covolume is always a number field. When considering subgroups of general Lie groups (which are not necessarily defined as a matrix groups) one has to use a linear representation of the group to take traces of elements. The most natural one is the adjoint representation. It turns out that for applications it is better, even for groups which have a natural lower-dimensional linear representation (such as the special linear groups formula_30), to always define the trace field using the adjoint representation. Thus we