A group of order n is said to be R-sequenceable if the nonidentity elements of the group can be listed in a sequence a,, a,, . . . , a,_ 1 such that the quotients a; ‘az, a; ’ a3, . , a;?,a,_ r, a.-_‘,a, are distinct. An abelian group is R*-sequenceable if it has an R-sequencing a,, a,, . . , a,, _ 1 such that a,_ ra, + r = ai for some i (subscripts are read modulo n - 1). Friedlander, Gordon and Miller (1978) showed that an R*-sequenceable Sylow 2-subgroup is a sufficient condition for a group to be R-sequenceable. In this paper we also show that all noncyclic abelian 2-groups are R*-sequenceable except for Tz x ZT4 and ZTz x ?Xz x T1.
['Patrick Headley']
R -sequenceability and R *-sequenceability of abelian 2-groups