In this paper, finite solvable groups satisfying the "n-prime hypothesis" are considered. Specifically, a bound on the number of irreducible character degrees of such a group is obtained when n = 2. The general situation is also considered, and generalizations of the n-prime hypothesis are analyzed.
Given a numerical semigroup S = a1, a2, . . . , at and s ∈ S, we consider the factorization s = c1a1 +c2a2 +· · ·+ctat where ci ≥ 0. Such a factorization is maximal if c1 +c2 +· · ·+ct is a maximum over all such factorizations of s. We show that the number of maximal factorizations, varying over the elements in S, is always bounded. Thus, we define dmax(S) to be the maximum number of maximal factorizations of elements in S. We study maximal factorizations in depth when S has embedding dimension less than four, and establish formulas for dmax(S) in this case.The next example demonstrates how we can easily compute the maximal denumerant of all basic semigroups with a fixed multiplicity.Example 4.5. Let S = 7, a 2 , a 3 be a basic semigroup with multiplicity a 1 = 7. Using Proposition 4.3, we carry out the following steps:
In this paper, we consider solvable groups that satisfy the twoprime hypothesis. We prove that if G is such a group and G has no nonabelian nilpotent quotients, then |cd(G)| ≤ 462,515. Combining this result with the result from part I, we deduce that if G is any such group, then the same bound holds.
A patient with retroperitoneal metastatic uterine adenocarcinoma resulting in symptomatic occlusion of the inferior vena cava underwent palliative endovascular stent reconstruction and subsequent radiation therapy. She then developed sepsis and massive lower gastrointestinal bleeding. Computed tomography (CT) and cavography demonstrated a fistulous communication between the duodenum and the stented segment of inferior vena cava. Deployment of endovascular stent graft devices successfully occluded the fistulous communication and resulted in clinical improvement.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.