Correlation between $E$-groups and properties of $n$-multiplications on Abelian groups

O. A. Karpov

Moscow State Pedagogical University, Moscow, Russia

Abstract: In this paper, we consider multilinear maps of an Abelian group into itself ($n$-multiplications) and their properties. We obtain equivalent conditions for an Abelian group to be an $E$-group in terms of $n$-multiplications. A correlation between properties of $n$-multiplications on the Abelian group at various $n$ is found.

UDC: 512.541

 English version: Journal of Mathematical Sciences (New York), 2021, 259:4, 420–426