The space of locally elliptic subgroups of a locally compact group

被引:0
作者
Gouiaa, Marwa [1 ]
Kammoun, Yousra [1 ]
机构
[1] Sfax Univ, Fac Sci Sfax, Dept Math, BP 1171, Sfax 3000, Tunisia
关键词
Chabauty topology; Locally compact group; locally elliptic group; locally elliptic radical; Noetherian group; CLOSED SUBGROUPS;
D O I
10.1080/00927872.2024.2404702
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a locally compact group. We denote by Sub(G) the space of closed subgroups of G equipped with the Chabauty topology. A closed subgroup H of G is called locally elliptic if every compact subset of H is contained in a compact subgroup. In this paper we establish that the subset SubLE(G) of closed locally elliptic subgroups of G is Chabauty-closed if and only if the set compn(G) consisting of the n-tuples of elements of G contained in a common compact subgroup, is closed in the Cartesian product Gn, for every nonnegative integer n. Moreover, we prove that the subspace SubLE(G) is Chabauty-closed in the case when the group G contains an open normal locally elliptic subgroup.
引用
收藏
页码:1202 / 1216
页数:15
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