5 papers
Finite approximation of free groups I: the -inverse cover problem
K. Auinger, J. Bitterlich, M. Otto
For a finite connected graph with set of edges , a finite -generated group is constructed such that the set of relations satisfied by (with a…
Combinatorial skeletons of 2-cobordism and annular categories with applications to equational logic
Karl Auinger, Mikhail Volkov
We introduce a complete set of combinatorial data that encode the category of all -cobordisms. As an application, we show that the local monoids of $2\mathfrak…
Cross-connection structure of locally inverse semigroups
P. A. Azeef Muhammed, M. V. Volkov, K. Auinger
Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterise the categories that correspond to locally inverse semigroups in the re…
-inverse monoids as algebraic structures in enriched signature
K. Auinger, G. Kudryavtseva, M. B. Szendrei
Every -inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its -class. In this enriched signature, the class of all -…
Formations of finite groups with the M. Hall property
Karl Auinger, Alexander Bors
The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of s…