On polynomial functions on squarefree expanded groups
Sprache des Vortragstitels:
71st Workshop on General Algebra (AAA71) together with 21st Conference for Young Algebraists (CYA21)
Sprache des Tagungstitel:
We show that on a finite expanded group whose order is squarefree and whose congruence lattice forms a chain every commutator preserving function is polynomial. This generalizes a previous result by E.~Aichinger and P.~Mayr that characterizes the polynomially inequivalent expansions of groups whose orders are a product of $2$ distinct primes.
Still we do not have a proof for P.~M.~Idziak's conjecture that each squarefree group has only finitely many polynomially inequivalent expansions.