Lower bounds for the number of local nearrings on groups of order $p^3$

Maryna Iuriivna Raievska; Iryna Iuriivna Raievska

Vol. 29 No. 2 (2024)

Regular Articles

Lower bounds for the number of local nearrings on groups of order $p^3$

Published 2024-10-04

Maryna Iuriivna Raievska
Iryna Iuriivna Raievska

Maryna Iuriivna Raievska
Institute of Mathematics of NAS of Ukraine, Ukraine

Iryna Iuriivna Raievska
Institute of Mathematics of NAS of Ukraine, Ukraine

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Abstract

Lower bounds for the number of local nearrings on groups of order $p^3$ are obtained. On each non-metacyclic non-abelian or metacyclic abelian groups of order $p^3$ there exist at least $p+1$ non-isomorphic local nearrings.

Keywords

Local nearring, $p$-group, metacyclic group, non-metacyclic group

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