Local nearrings with generalized quaternion multiplicative group

Abstract

A not necessarily zero-symmetric nearring R with identity is called local if the set of all non-invertible elements of R forms a subgroup of its additive group. The local nearrings whose multiplicative group is generalized quaternion are described. In particular, it is proved that their additive groups are abelian of types (3,3), (2,2,2,2), (2,2,4), (2,2,2,2,2) and (2,2,2,4). Keywords: Local nearring, Multiplicative group, Generalized quaternion group, Factorized group Mathematics Subject Classification (2000): 16N20, 16U60, 20M25