Abstract We show that a group is hyperbolic relative to strongly shortcut groups itself shortcut, thus obtaining new examples of groups. The proof relies on result independent interest: we every relatively acts properly and cocompactly graph in which the parabolic subgroups act convex subgraphs.

We show that if G is a strongly minimal finitely axiomatizable group, the division ring of quasi-endomorphisms of G must be an infinite finitely presented ring. Questions about finite axiomatizability of first order theories are nearly as old as model theory itself and seem at first glance to have a fairly syntactical flavor. But it was in order to show that totally categorical theories cannot ...

In this paper, we provide a survey (both theoretical and computational) of the conditions for determining which finite p -groups are strongly flat. Let m(G) denote the maximum size of an irredundant generating set of a group G . Then, a group G is strongly flat if m(G) is strictly greater than m(H) for all proper subgroups H of G . For example, J. Whiston has shown in his dissertation that all ...

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the ...