Background: Central hyperthyroidism is characterized by elevated free thyroid hormone and unsuppressed stimulating (TSH) this laboratory feature includes TSH-secreting pituitary adenoma (TSHoma) resistance to β (RTHβ). combined with Graves' disease (GD) has been rarely reported. Case Report: We describe three patients TSHoma GD one patient RTHβ adenoma. These showed hormone, while TSH level was...

We give various estimates of the minimal number of self-intersections of a nontrivial element of the kth term of the lower central series and derived series of the fundamental group of a surface. As an application, we obtain a new topological proof of the fact that free groups and fundamental groups of closed surfaces are residually nilpotent. Along the way, we prove that a nontrivial element o...