Emma Leppälä, Markku Niemenmaa
On finite commutative loops which are centrally nilpotent

Abstract:Let $Q$ be a finite commutative loop and let the inner mapping group $I(Q) \cong C_{p^n} \times C_{p^n}$, where $p$ is an odd prime number and $n \geq 1$. We show that $Q$ is centrally nilpotent of class two.

Keywords: loop; inner mapping group; centrally nilpotent loop

DOI: DOI 10.14712/1213-7243.2015.113
AMS Subject Classification: 20N05 20D15