Rosłanowski and Shelah [Small-large subgroups of the reals, Math. Slov. 68(3) (2018) 473–484] asked whether every locally compact non-discrete group has a null but non-meager subgroup, and conversely, whether it is consistent with ZFC that in every locally compact group a meager subgroup is always null. They gave affirmative answers for both questions in the case of the Cantor group and the reals. In this paper, we give affirmative answers for the general case.

中文翻译：

---

回答 Rosłanowski 和 Shelah 的问题

Rosłanowski 和 Shelah [实数的小型大型子群，数学。斯洛夫。 68(3) (2018) 473–484] 询问每个局部紧致非离散群是否有一个零但非微薄的子群，反之，是否与ZFC在每一个局部紧群中，一个微弱的子群总是空的。在康托群和实数的情况下，他们对这两个问题都给出了肯定的回答。在本文中，我们对一般情况给出肯定的答案。