群表示的非球面性和图解简化的新检验
A new test for asphericity and diagrammatic reducibility of group presentations
摘要：
提出了一种研究群表示的非球面性和图解约化的新方法。我们的测试可以应用于证明图解约简的情况下，经典的重量测试失败。我们用这个准则推广了J.Howie和S.M. Gersten上的非球面的LOTs和Adian介绍，并得出新的结果的可解性方程组。我们还使用我们的方法来调查一个猜想S.V.Ivanov有关的Kaplansky的问题零因子：我们加强Ivanov的结果，局部可指示群，并证明了一个弱版本的猜想。
英文摘要：
We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian presentations, and derive new results on solvability of equations over groups. We also use our methods to investigate a conjecture of S.V. Ivanov related to Kaplansky's problem on zero divisors: we strengthen Ivanov's result for locally indicable groups and prove a weak version of the conjecture.
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