Commensurability and elementary equivalence of polycyclic groups

被引：3
|
作者：
Raphael, D [1 ]
机构：
[1] UNIV SAO PAULO,INST MATEMAT & ESTAT,BR-05389970 SAO PAULO,BRAZIL
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 1996年 / 53卷 / 03期
关键词：
D O I：
10.1017/S0004972700017184
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that two polycyclic-by-finite groups G and H, satisfying the same sentences with one alternation of quantifiers, are commensurable. In fact we show something stronger: given n > 1 there is a subgroup H-n of H and a subgroup G(n) of G such that H-n similar or equal to G, G(n) similar or equal to H and the indices [G:G(n)] and [H:H-n] are finite and prime to n.
引用
收藏
页码：425 / 439
页数：15
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