R-sequenceability and R*-sequenceability of abelian 2-groups

Abstract

A group of order n is said to be R-sequenceable if the nonidentify elements of the group can be listed in a sequence a1,a2,...,an-1 such that the quotients a-11a2,a-12a3,...,a-1n-2an-1,a-1n-1a1 are distinct. An abelian group is R*-sequenceable if it has an R-sequencing a1,a2,...,an-1 such that ai-1ai+1=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 2 x 4 and 2 x 2 x 2.