On R*-sequenceability and symmetric harmoniousness of groups

We introduce a special harmoniousness called symmetric harmoniousness of groups and extend the R^*-sequenceability of abelian groups to nonabelian groups. We prove that the direct product of an R^*-sequenceable group of even order with a symmetric harmonious group of odd order is R^*-sequenceable. Examples of nonabelian R^*-sequenceable groups and nonabelian symmetric harmonious groups are given. It is shown that the nonabelian groups of order 3q (q prime) are symmetric harmonious. © 1994 John Wiley & Sons, Inc.