Term functions on non-Abelian groups of order \(pq\). (English) Zbl 0531.08002

Lausch, Hans

Arch. Math., Brno 18, 219-220 (1982).

It is proved that the number of n-variable term functions over the nonabelian group of order pq \((p>q\) primes), i.e. the order of the n- generator free group in the variety generated by this group, is \(q^ np^{(n-1)q^ n+1}.\) This generalizes a result of Y. Coufalová obtained for the case \(p=3\), \(q=2\) [Arch. Math., Brno 16, 67-79 (1980; Zbl 0456.08006)].

Reviewer: P.P.Pálfy

MSC:

08A40	Operations and polynomials in algebraic structures, primal algebras
20D60	Arithmetic and combinatorial problems involving abstract finite groups
20E10	Quasivarieties and varieties of groups

Keywords:

number of term functions; order of n-generator free group

Citations:

Zbl 0456.08006