32 citations · 65 across the 10 of their papers we have counts for
12 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…
The geometry of profinite graphs revisited
K. Auinger
For a formation of finite groups, tight connections are established between the pro--topology of a finitely generated free group and the geometry o…
The Finite Basis Problem for Kauffman Monoids
Karl Auinger, Yuzhu Chen, Xun Hu +2
We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid a…
Unary enhancements of inherently nonfinitely based semigroups
Karl Auinger, Igor Dolinka, Tatiana V. Pervukhina +1
We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semig…
On the variety of strict pseudosemilattices
K. Auinger, L. Oliveira
A new model, in terms of finite bipartite graphs, of the free pseudosemilattice is presented. This will then be used to obtain several results about the variety SPS of all strict p…
On the power pseudovariety
K. Auinger
Some new semantic and syntactic characterizations of the members of the power pseudovariety are obtained. This leads in particular to new algorithms for deciding mem…
Krohn--Rhodes complexity of Brauer type semigroups
Karl Auinger
The Krohn--Rhodes complexity of the Brauer semigroup and of the annular semigroup is computed.
Matrix identities involving multiplication and transposition
Karl Auinger, Igor Dolinka, Mikhail Volkov
We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no fini…