У статтi здiйснено огляд сучасного стану дослiдження скiнченних локальних майже-кiлець, а саме їх похiдних структур-адитивної та мультиплiкативної груп. Наведено класифiкацiю локальних майжекiлець, порядок яких не перевищує 32. Ключовi слова: локальне майже-кiльце, майже-кiльце з одиницею, адитивна група, мультиплiкативна група.
It is proved that the additive group of every semidistributive nearring R with an identity is abelian and if R has no elements of order 2 , then the nearring R actually is an associative ring.
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.
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