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

  • 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
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.

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How to Cite
(1)
Raievska I., Raievska M. Local Nearrings on Finite Non-Abelian $2$-Generated $p$-Groups. Carpathian Math. Publ. 2020, 12 (1), 199-207.