In this paper, the structure of uncountable groups with finitely many normalizers of large subgroups is studied and the connections between this property and other natural finiteness conditions on large subgroups of uncountable groups are investigated. In particular, groups in which every large subgroup is close to be normal with the only obstruction of a finite section and groups with finitely many commutator subgroups of large subgroups are considered. Moreover, groups with a finite covering consisting of groups with normal large subgroups are studied.

中文翻译：

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具有有限多个大子群标准化子的不可数群

本文研究了具有有限多个大子群归一化子的不可数群的结构，并研究了该性质与不可数群大子群上其他自然有限性条件之间的联系。特别地，考虑其中每个大子群都接近正规且仅有有限部分的阻碍的群以及具有有限多个大子群的换向器子群的群。此外，还研究了由具有正常大子群的群组成的具有有限覆盖的群。