Gruppenuniversalität und Homogenisierbarkeit
The authors use model theory to prove that, for very general classes \({\mathcal C}\) of structures: (1) every group G is the full automorphism group of some \(C\in {\mathcal C}\), (2) every \(C\in {\mathcal C}\) may be embedded in a homogeneous \(H\in {\mathcal C}\). The results unify numerous results from the literature. The authors discuss the applicability of the results to groups, projective planes, affine planes, (m,n)-planes, (k,m,n)- geometries, generalized n-corners (or vertices), k-nets, (k,n)-Steiner systems, LP-spaces, covering geometries, ''magmas'' of type \(\tau\), \(\theta\)-algebras of type \(\tau\), commutative loops and quasigroups, commutative algebras of type \(\tau\) over a commutative field, and commutative division algebras over a commutative field.
scientific article; zbMATH DE number 3943792
scientific article