Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect product when the twisting homomorphism acts diagonally on a direct product, as well as for the case when the extending group is a direct product. We give applications of these results in the case of generalized dihedral groups and classic dihedral groups $D_{2n}$. For $D_{2n}$ we give a complete description of semidirect decompositions and values of minimal permutation degrees

Copper-Catalyzed Arylation of 1\u3cem\u3eH\u3c/em\u3e-Perfluoroalkanes

A general method has been developed for arylation of readily available 1H-perfluoroalkanes. The method employs aryl iodide and 1H-perfluoroalkane reagents, DMPU solvent, TMP2Zn base, and a copper chloride/phenanthroline catalyst. Preliminary mechanistic studies are reported