The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group In+1(π,w) and the closed manifold subgroup Cn+1(π,w) are equal in dimensions n+1 ≥ 6, for any finitely-presented group π and any orientation character w : π → Z/2. This answers a quest...

Differential Galois theory, the theory of strongly normal extensions, has unfortunately languished. This may be due to its reliance on Kolchin’s elegant, but not widely adopted, axiomatization of the theory of algebraic groups. This paper attempts to revive the theory using a differential scheme in place of those axioms. We also avoid using a universal differential field, instead relying on a c...

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...

Abstract Given a pointed metric space M , we study when there exist n -dimensional linear subspaces of $$\mathrm {Lip}_0(M)$$ Lip 0 ( M ) consisting strongly norm-attaining Lipschitz functionals, ...

In this paper we study finite groups which possess a strongly pembedded subgroup for some prime p. Suppose that p is a prime. A subgroup H of the finite group G is said to be strongly p-embedded in G if the following two conditions hold. (i) H < G and p divides |H|; and (ii) if g ∈ G \H , then p does not divide |H ∩H|. One of the most important properties of strongly p-embedded subgroups is tha...