Let X be a right-angled hyperbolic building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of grou...

It is shown that Aut(L ~ is naturally isomorphic to Aut(L) x Aut(Q) when L is a directly and exponentially indecomposable lattice, Q a non-empty connected poset, and one of the following holds: Q is arbitrary but L is a jm-lattice, Q is finitely factorable and L is complete with a join-dense subset of completely join-irreducible elements, or L is arbitrary but Q is finite. A problem of J6nsson ...

Let M be a connected complex manifold of dimension n and let Aut(M) denote the group of holomorphic automorphisms of M . The group Aut(M) is a topological group equipped with the natural compact-open topology. We are interested in the problem of characterizing M by Aut(M). This problem becomes particularly intriguing when Aut(M) is infinite-dimensional. Let, for example, M = C and suppose that ...

Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study Tits alternative and virtual derived length solvable subgroups $\operatorname{Aut}(X)$.

We investigate the automorphisms of some $$\kappa $$ -existentially closed groups. In particular, we prove that Aut(G) is union subgroups level preserving and $$|Aut(G)|=2^{\kappa }$$ whenever inaccessible G unique group cardinality . Indeed, latter result a byproduct an argument showing that, for any uncountable limit regular representation length with countable base, have $$|Aut(G)|=\beth _{\...

We use the automorphism group Aut(H), of holes in the lattice L8 = A2 ⊕ A2 ⊕ D4, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, L4 = A2 ⊕ A2, enters the construction because a subgroup of Aut(L4) is isomorphic to Aut(H). The lattices L8 and L4, when glued together through this relationship, provide an alternative construction of the lamin...

This study aimed to examine the interaction effect of response medium (i.e., write down ideas and orally report ideas) and working memory capacity (WMC) on creative idea generation. Participants (N = 90) with higher or lower WMC were asked to solve Alternative Uses Task (AUT) problems in the condition of writing down or speaking out ideas. The results showed that fluency of AUT performance was ...