A note on the derived quotients of certain cyclically presented groups

被引：4
|
作者：
Solan, Ikhalfani [1 ]
Stoddart, Devon [2 ]
机构：
[1] Univ West Indies, Dept Math & Comp Sci, Kingston, Jamaica
[2] Univ Coll Cayman Isl, Dept Comp Sci & Technol, George Town, Cayman Islands
来源：
JOURNAL OF INTERDISCIPLINARY MATHEMATICS | 2008年 / 11卷 / 04期
关键词：
Derive quotients; cyclically presented groups; Alexander polynomial;
D O I：
10.1080/09720502.2008.10700578
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the derived quotients, An, of the cyclically presented groups G(n)= < x(i)|x(i+1)(-1)x(i+2)x(i+1)(-1) x(i+2)x(i)x(i+1)(-1)x(i) = 1 >(n) and show that A(n) is 2-generated, isomorphic to Zd(1) x Zd(2), d(2)|d(1) with order o(A(n)) = 2(n+1) (1 - cos n theta) where theta = arccos (sic). We also prove that o(A(n)) satisfies the recurrence relation a(n) = 5a(n-1) - 10a(n-2) + 8a(n-3).
引用
收藏
页码：521 / 524
页数：4
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