Локальні майже-кільця та ендоциклічні групи малих порядків

Nearrings are generalization of associative rings, in which the additive group can be non-abelian, and addition is connected with multiplication at least one distributive law, left or right. In this sense local nearrings are generalization of local rings. The package SONATA of the computer algebra system GAP contains a library of all non-isomorphic nearrings of order at most 15 and nearrings with a unity of order at most 31, among which 698 are local. However, the classification of nearrings of higher orders requires much more complex calculations. The classification of nearrings with identity (up to order 32) and local nearrings (of orders 32 and 64) on endocyclic additive groups is given. Moreover, some information concerning these nearring from the LocalNR and SONATA packages of GAP is presented.