A topological group G with $|G|>1$ is called d-independent if for every subgroup S of G with $|S|<2^{\omega }$, one can find a countable dense subgroup H of G such that $S\cap H=\{e\}$. Therefore, d-independent groups are separable and have cardinality at least $2^{\omega }$. Our main result is a purely algebraic characterization of d-independence in the class of compact metrizable abelian groups. We prove that a compact metrizable abelian group G with $|G|>1$ is d-independent if and only if for every integer $m\ge 1$, either $|mG|=2^{\omega }$ or $|mG|=1$. This characterization implies that a compact metrizable abelian group is d-independent if and only if it is maximally fragmentable [Comfort and Dikranjan (2014) [4]] iff G an M-group as defined by Dikranjan and Shakhmatov (2016) in [7].

Also we present a characterization of separable metrizable d-independent abelian groups and show that products of separable topological groups can often be d-independent, even if the factors fail to be d-independent.

甲拓扑群G ^与$|G|>1$被称为d无关，若对所有子群小号的ģ与$|\mathrm{S。}|<2^{\omega }$，可以发现一个可数稠密子群ħ的ģ使得$\mathrm{S。}\cap H=\{\mathrm{电子}\}$. 因此，在独立团是可分离的，并至少有基数$2^{\omega }$. 我们的主要结果是对紧凑可度量阿贝尔群类中d独立性的纯代数表征。我们证明了一个紧度量阿贝尔群G ^与$|G|>1$与d无关当且仅当对于每个整数$米\ge 1$， 任何一个 $|米G|=2^{\omega }$ 或者 $|米G|=1$. 这种表征意味着一个紧凑的可计量阿贝尔群是d独立的，当且仅当它是最大可碎片化的[Comfort and Dikranjan (2014) [4]] iff G是由 Dikranjan 和 Shakhmatov (2016) 在 [7 ]中定义的M 群]。

此外，我们还介绍了可分离的可计量d独立阿贝尔群的表征，并表明可分离拓扑群的乘积通常可以是d独立的，即使这些因子不能是d独立的。