Doubly sequenceable groups (Q6576929)

The reviewed article is concerned with the examination of the so-called \textit{doubly sequenceable groups} (\textit{D-sequenceable} for short) and especially with discovering which classes of groups are of this sort. It is proved that if a group is abelian, of odd order, (R-)sequenceable or terraceable, then it is D-sequenceable.\N(For some interesting examples of such results, see Theorem 8 and 17.)\N\NMoreover, it is shown that the direct product of an abelian group with a group of odd order as well as the direct product of an abelian group with a sequenceable group is necessarily doubly sequenceable in both cases (see Theorem 4).\N\NAll of this is in regard to the well-known \textit{double sequencing conjecture} which claims that all groups are D-sequenceable.\N\NNote that any group of odd order is solvable by the famous Feit-Thompson theorem, however the present paper does \textit{not} contain a result of the type that all solvable groups are D-sequenceable.