Bezushchak, O. O.O. O.Bezushchak2026-06-302026-06-302019Bezushchak, O. O. (2019). On diagonal locally SL-groups. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 8–11. https://doi.org/10.17721/1812-5409.2019/4.110.17721/1812-5409.2019/4.1https://ir.library.knu.ua/handle/15071834/26287Let N be the set of natural numbers. Let F be a field. In [1], we introduced a class of groups SL^p_s (F) and GL^p_s (F) of periodic infinite (N \times N)–matrices that correspond to a Steinitz number s: In this paper we introduce a wider class of diagonal locally SL–groups and GL–groups and study their relations with locally matrix algebras. In particular, we show that every separable–diagonal locally SL–group (respectively GL–group) is isomorphic to a group SL^p_s (F) (respectively GL^p_s (F)). Pages of the article in the issue: 8 - 11 Language of the article: EnglishLet N be the set of natural numbers. Let F be a field. In [1], we introduced a class of groups SL^p_s (F) and GL^p_s (F) of periodic infinite (N \times N)–matrices that correspond to a Steinitz number s: In this paper we introduce a wider class of diagonal locally SL–groups and GL–groups and study their relations with locally matrix algebras. In particular, we show that every separable–diagonal locally SL–group (respectively GL–group) is isomorphic to a group SL^p_s (F) (respectively GL^p_s (F)). Pages of the article in the issue: 8 - 11 Language of the article: Englishenlocally matrix algebraSteinitz numberdiagonal embeddingperiodic matrixСтаття