Abstract

Let \(\mathcal{K}\) be a class of groups closed under taking subgroups, direct products of a finite number of factors, and quotient groups. Let also \(G\) be a generalized direct product of two groups with amalgamated subgroups. We obtain necessary and sufficient conditions for \(G\) to be residually a \(\mathcal{K}\)-group. These results generalize and strengthen the known conditions for the residual finiteness of the group \(G\).

中文翻译：

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群广义广义乘积的剩余性质

摘要

令\（\ mathcal {K} \）为一类在子组，有限数量因子的直接乘积和商组下封闭的组。也让\（G \）是两个具有合并子组的组的广义直接乘积。我们获得了必要的充分条件，使得\（G \）成为\（\ mathcal {K} \）-组。这些结果推广并加强了\（G \）群的剩余有限性的已知条件。