Nik Ruškuc

Research - selected open problems

Here is a selection of problems I would like to know answers to. If you have any ideas please contact me.

Problem 1. Does there exist a non finitely presented semigroup which is a disjoint union of two free semigroups of rank 2?

Problem 2. Does every FA presentable semigroup satisfy a non-trivial semigroup identity? (For background see Section 7 in this paper.)

Problem 3. In a strongly rational pattern class of permutations, does the set of all simple permutations necessarily have a rational generating function? (For background see Section 9 in arXiv:1202.1833.)

Problem 4. Can every finitely presented semigroup be embedded in a finitely presened bisimple semigroup?