长度为4的正相关群的周期性呈现的Tits替代

Pub Date : 2022-03-08 DOI:10.1515/jgth-2021-0131

Shaun Isherwood, Gerald Williams

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引用次数: 1

摘要

摘要:我们研究了Bogley和Parker在定义参数中引入的同余(a)， (B)， (C)系统中具有长度为4的正相关的循环呈现群的Tits替代。除了(B)成立，(A)和(C)都不成立的情况外，我们证明Tits选项是满足的;在其余情况下，我们证明当循环表示的生成器数量最多为20时，Tits备选方案是满足的。

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On the Tits alternative for cyclically presented groups with length-four positive relators

Abstract We investigate the Tits alternative for cyclically presented groups with length-four positive relators in terms of a system of congruences (A), (B), (C) in the defining parameters, introduced by Bogley and Parker. Except for the case when (B) holds and neither (A) nor (C) hold, we show that the Tits alternative is satisfied; in the remaining case, we show that the Tits alternative is satisfied when the number of generators of the cyclic presentation is at most 20.

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