Local nearrings on finite non-abelian $2$-generated $p$-groups

I.Yu. Raievska; M.Yu. Raievska

doi:10.15330/cmp.12.1.199-207

Local nearrings on finite non-abelian $2$ -generated $p$ -groups

Authors

I.Yu. Raievska Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine
M.Yu. Raievska Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine

https://doi.org/10.15330/cmp.12.1.199-207

Keywords:

finite

$p$ -group, local nearring

Published online: 2020-06-29

Abstract

It is proved that for ${p>2}$ every finite non-metacyclic $2$ -generated p-group of nilpotency class $2$ with cyclic commutator subgroup is the additive group of a local nearring and in particular of a nearring with identity. It is also shown that the subgroup of all non-invertible elements of this nearring is of index $p$ in its additive group.