Abstract
AbstractWe 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.
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