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 ...

Certain subgroups of the groups Aut(Fn) of automorphisms of a free group Fn are considered. Comparing Alexander polynomials of two poly-free groups Cb+4 and P4 we prove that these groups are not isomorphic, despite the fact that they have a lot of common properties. This answers the question of Cohen-Pakianathan-Vershinin-Wu from [8]. The questions of linearity of subgroups of Aut(Fn) are consi...

Let $L_{n}$ be the free Lie algebra of rank $n$ over a field $K$ characteristic zero, $L_{n,c}=L_{n}/(L_{n}''+\gamma_{c+1}(L_{n}))$ metabelian nilpotent class $c$ algebra, and $F_{n}=L_{n}/L_{n}''$ generated by $x_1,\ldots,x_n$ zero. We call polynomial $p(X_n)$ in these algebras {\it symmetric} if $p(x_1,\ldots,x_n)=p(x_{\pi(1)},\ldots,x_{\pi(n)})$ for each element symmetric group $S_n$. The se...