0000000000653025
AUTHOR
Peter Hubert
Local Near-Rings and Triply Factorized Groups
Abstract Groups G of the form G = AB = AM = BM for two subgroups A and B of G and a normal subgroup M of G with A ∩ M = B ∩ M = 1 are called triply factorized and play an important role in the theory of factorized groups. In this paper, a method to construct triply factorized groups with non-abelian M using local near-rings is introduced.
Local nearrings with dihedral multiplicative group
AbstractA not necessarily zero-symmetric nearring R with a unit element is called local if the set of all non-invertible elements of R forms a subgroup of the additive group of R. It is proved that every local nearring whose multiplicative group is dihedral is finite and its additive group is either a 3-group of order at most 9 or a 2-group of order at most 32.