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

Iryna Iu. Raievska; Maryna Iu. Raievska

doi:10.15330/cmp.12.1.199-207

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

Rings and Algebras 2020-07-01 v1

Authors: Iryna Iu. Raievska , Maryna Iu. Raievska

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Abstract

Finite non-abelian non-metacyclic $2$ -generated $p$ -groups ( ${p>2}$ ) of nilpotency class $2$ with cyclic commutator subgroup which are the additive groups of local nearrings are described. It is shown that the subgroup of all non-invertible elements is of index $p$ in its additive group.

Keywords

local nearrings finite p-groups non-abelian 2-generated nilpotency class 2 cyclic commutator subgroup non-invertible elements

Cite

@article{arxiv.1906.02949,
  title  = {Local nearrings on finite non-abelian $2$-generated $p$-groups},
  author = {Iryna Iu. Raievska and Maryna Iu. Raievska},
  journal= {arXiv preprint arXiv:1906.02949},
  year   = {2020}
}

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