A map on a group is not necessarily an automorphism on the group. In this paper we study the necessary and sufficient conditions for a map on a non-split metacyclic p-group to be an automorphism, where we only consider p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We consider the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then use the relations and the regularity of the non-split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism.
Three new fully dehydrogenated naphthylisoquinoline alkaloids, the 7,1'-coupled ent-dioncophylleine A (3a), the likewise 7,1'-coupled 5'-O-demethyl-ent-dioncophylleine A (4), and the 7,8'-linked dioncophylleine D (5), have been isolated from the leaves of the recently described Malaysian highland liana Ancistrocladusbenomensis. All of them lack an oxygen function at C-6; this so-called Dioncophyllaceae-type structural subclass had previously been found only in naphthylisoquinoline alkaloids from West and Central African plants. Moreover, compounds 3a and 4 are the first fully dehydrogenated, i.e., only axially chiral, naphthylisoquinoline alkaloids of this type that are optically active; compound 5, by contrast, is fully racemic, due to its configurationally unstable biaryl axis. The structural elucidation was achieved by spectroscopic and chiroptical methods. Biological activities of these alkaloids against different protozoan parasites are described.