We present a metric condition $\TTMetric$ which describes the geometry of classical small cancellation groups and applies also to other known classes of groups such as two-dimensional Artin groups. We prove that presentations satisfying condition $\TTMetric$ are diagrammatically reducible in the sense of Sieradski and Gersten. In particular, we deduce that the standard presentation of an Artin group is aspherical if and only if it is diagrammatically reducible. We show that, under some extra hypotheses, $\TTMetric$-groups have quadratic Dehn functions and solvable conjugacy problem. In the spirit of Greendlinger's lemma, we prove that if a presentation P = 〈X| R〉 of group G satisfies conditions $\TTMetric -C'(\frac {1}{2})$, the length of any nontrivial word in the free group generated by X representing the trivial element in G is at least that of the shortest relator. We also introduce a strict metric condition $\TTMetricStrict$, which implies hyperbolicity.

我们提出了一个度量条件$\TTMetric$，它描述了经典小抵消群的几何形状，也适用于其他已知的群类别，例如二维Artin群。我们证明满足条件$\TTMetric$的表示在 Sieradski 和 Gersten 的意义上是图解可约的。特别是，我们推断出 Artin 群的标准表示是非球面的当且仅当它是图解可约的。我们证明，在一些额外的假设下，$\TTMetric$ -groups具有二次 Dehn 函数和可解的共轭问题。根据格林德林格引理的精神，我们证明如果一个表示P = 〈X | 组的R〉G满足条件$\TTMetric -C'(\frac {1}{2})$ ，表示G中平凡元素的X生成的自由群中任意非平凡词的长度至少是最短关系者的长度。我们还引入了一个严格的度量条件$\TTMetricStrict$，这意味着双曲线。