On the hyperbolicity of small cancellation groups and one-relator groups
On the hyperbolicity of small cancellation groups and one-relator groups
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关于小抵消群和单相关群的双曲性
DOI：
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发表时间：
1998
期刊：
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通讯作者：
P. Schupp
中科院分区：
文献类型：
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作者：
S. Ivanov;P. Schupp
在本文中，与满足 C(p)T 的映射（= 有限平面连通和单连通 2-complex）相关的结果表明，有限生成的一个关系器群 G 其约简关系器 R 的形式为 R == aT0aT1 。 。 。 aTn−1，其中单词 Ti 是不同的，并且没有出现字母 a ±1，当且仅当在自由群中存在 (1) n = 2 并且 T0T -1 1 是真幂时，aTn−1 不是双曲线； (2) n = 3，对于某些 i，TiT −1 i+1TiT −1 i+2 = 1 成立（下标 mod 3）； (3) n = 4，对于某些 i，TiT −1 i+1Ti+2T −1 i+3 = 1 成立（下标 mod 4）。
In the article, a result relating to maps (= finite planar connected and simply connected 2-complexes) that satisfy a C(p)T it is shown that a finitely generated onerelator group G whose reduced relator R is of the form R ≡ aT0aT1 . . . aTn−1, where the words Ti are distinct and have no occurrences of the letter a ±1, is not hyperbolic if and only if one has in the free group that (1) n = 2 and T0T −1 1 is a proper power; (2) n = 3 and for some i it is true (with subscripts mod 3) that TiT −1 i+1TiT −1 i+2 = 1; (3) n = 4 and for some i it is true (with subscripts mod 4) that TiT −1 i+1Ti+2T −1 i+3 = 1.