Abstract
We prove that a topological Abelian locally compact group with generalized minimality condition for closed subgroups is a group of one of the following types: 1) a group with minimality condition for closed subgroups, 2) an additive group of theJ p -ring of integerp-adic numbers, 3) an additive groupR p of the field ofp-adic numbers (p is a prime number).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. M. Glushkov, “Locally bicompact groups with minimality condition for closed subgroups,”Ukr. Mat. Zh.,8, No. 2, 132–139 (1956).
V. M. Glushkov, “On the theory of special locally bicompact groups,”Ukr. Mat. Zh.,11, No. 4, 347–350 (1959).
V. A. Khoteev and V. S. Charin, “Groups with minimality condition for subgroups,”Mat. Zametki,2, No. 1, 3–10 (1967).
A. G. Kurosh,Group Theory [in Russian], Nauka, Moscow (1967).
L. S. Pontryagin,Continuous Groups [in Russian], Nauka, Moscow (1973).
Additional information
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 398–409, March, 1999.
About this article
Cite this article
Charin, V.S. On the theory of groups with generalized minimality condition for closed subgroups. Ukr Math J 51, 444–454 (1999). https://doi.org/10.1007/BF02592481
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02592481