R-SEQUENCEABILITY AND R-ASTERISK-SEQUENCEABILITY OF ABELIAN 2-GROUPS

被引：9

作者：

HEADLEY, P ^{[1
]}

机构：

[1] UNIV MICHIGAN,DEPT MATH,ANN ARBOR,MI 48109

来源：

DISCRETE MATHEMATICS | 1994年 / 131卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0012-365X(94)90396-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A group of order n is said to be R-sequenceable if the nonidentity elements of the group can be listed in a sequence a1, a2, ..., a(n-1) such that the quotients a1(-1)a2, a2(-1)a3, ..., a(n-2)-1a(n-1), a(n-1)-1a1 are distinct. An abelian group is R*-sequenceable if it has an R-sequencing a1, a2, ..., a(n-1) such that a(i-1)a(i+1) = a(i) 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 F2 x F4 and F2 x F2 x F2.

引用

页码：345 / 350

页数：6