Commensurability and elementary equivalence of polycyclic groups
Commensurability and elementary equivalence of polycyclic groups
复制标题
多环群的可通约性和基本等价性
DOI：
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发表时间：
1996
影响因子：
0.7
通讯作者：
Deborah Raphael
中科院分区：
文献类型：
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作者：
Deborah Raphael
证明了满足相同句子的两个有限多圈群G和H是可交换的。事实上，我们证明了更强的东西：给定n > 1，存在H的子群Hn和G的子群Gn使得Hn <$G，Gn <$H，且指数[G：Gn]和[H：Hn]是有限的且与n互素。
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 Hn of H and a subgroup Gn of G such that Hn≃G, Gn≃H and the indices [G: Gn] and [H: Hn] are finite and prime to n.