Let Γ denote either the automorphism group of the free group of rank n ≥ 4 or the mapping class group of an orientable surface of genus n ≥ 12 with 1 boundary component, and let G be either the subgroup of IA-automorphisms or the Torelli subgroup of Γ, respectively. We prove that any subgroup of G containing [G,G] (in particular, the Johnson kernel in the mapping class group case) is finitely g...

BACKGROUND Predictive models for febrile neutropenia (FN) would be informative for physicians in clinical decision making. This study aims to validate a predictive model (Jenkin's model) that comprises pretreatment hematological parameters in early-stage breast cancer patients. PATIENTS AND METHODS A total of 428 breast cancer patients who received neoadjuvant/adjuvant chemotherapy without an...

We construct an infinite family of topologically slice knots that are not smoothly concordant to their reverses. More precisely, if $$\mathcal {T}$$ denotes the concordance group and $$\rho $$ is involution induced by string reversal, then {T}/ \text {Fix}(\rho )$$ contains infinitely generated free subgroup. The result remains true modulo subgroup with trivial Alexander polynomial.

Let x, y be two integer quaternions of norm p and l, respectively, where p, l are distinct odd prime numbers. What can be said about the structure of 〈x, y〉, the multiplicative group generated by x and y ? Under a certain condition which excludes 〈x, y〉 from being free or abelian, we show for example that 〈x, y〉, its center, commutator subgroup and abelianization are finitely presented infinite...

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, P-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizer a non-finitely-generated subgroup of the rational numb...

According to Thurston’s stability theorem, every group of C diffeomorphisms of the closed interval is locally indicable (i.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the group F2 ⋉ Z , although locally indicable, does not embed into Diff1+(]0, 1[). (Here F2 i...

Let L be a lattice in d-dimensional real Euclidean space V , and let σ be a polyhedral decomposition of V . If the cones of σ are generated by vectors in L, σ is called a (complete) fan in L (and we say σ is integral with respect to L). If each i-dimensional cone of σ is generated by i vectors, we say σ is simplicial. Associated to any fan σ in V is a toric variety, Xσ. In [7], Stembridge showe...

If G is a group, then subgroups A and B are commensurable if A ∩B has finite index in both A and B. The commensurator of A in G, denoted CommG(A), is {g ∈ G|(gAg−1) ∩A has finite index in both A and gAg−1}. It is straightforward to check that CommG(A) is a subgroup of G. A subgroup A is commensurated in G if CommG(A) = G. The centralizer of A in G is a subgroup of the normalizer of A in G which...

The generalization of the Magnus embedding [7] proved by Smelkin [9] may be stated as follows. Let L be a free group freely generated by the set x^iel) , and let R be a normal subgroup of L with G = L/R. If V is any variety of groups and n is the F-free group with free generating set the symbols [g,xj (geG, iel), then L/V(R) is embedded in the semidirect product II xi G (where the action of G o...