Groups of periodically
defined permutations on a countable set (in Russian)

V. V. Nazarchuk; V. I. Sushchansky

A class of groups consisting of almost periodic permutations is considered. These groups are parametrized by supernatural numbers. The conjugacy classes and normal structure of each group of this class are characterized.

1. Вершик А. М. Описание инвариантных мер для действий некоторых бесконечных групп. // Докл. АН СССР. – 1974. –Т. 218, № 4. – С. 749 – 752.

2. Залесский А.Е. Групповые кольца индуктивных пределов знакопеременных групп // Алгебра и анализ. –1990. – Т.2, № 6 –С.132–149.

3. Крошко Н.В., Сущанський В.I. Однорiдно симетричнi групи // Доп. НАН України. – 1993. – № 12. – С. 9–13.

4. Kroshko N.V., Sushchansky V.I. Direct limits of symmetric and alternating groups with strictly diagonal embeddings // Archiv der Mathematik. – 1998. –V.71. – P.173–182.

5. Gschwend T., Kegel O. H. On the group of weak automorphisms of a family of equivalence relations // Algebra and operator theory.– 1997.– P.237–248.

6. Brawley J. V., Schnibben G. E. Infinite algebraic extensions of finite fields.– Contemporary mathematics, Vol. 95.– Providence, Rhode Island:–Amer. Math. Soc. – 1992.– 104 p.

7. Назарчук В.В., Сущанський В.I. Групи перiодично визначених пiдстановок. // Доп. НАН України. – 2003. – № 3.– С.26–30.

8. Bhattacharjee M., Macpherson D., Möller R.G., Neumann P. Notes on Infinite Permutation Groups. – New Delhi: Hindustan Book Agency.– 1997. – 202 p.

	Groups of periodically defined permutations on a countable set (in Russian)
Author	V. V. Nazarchuk, V. I. Sushchansky Taras Shevchenko National University of Kyiv, Ukraine, Silesian University of Technology, Gliwice, Poland
Abstract	A class of groups consisting of almost periodic permutations is considered. These groups are parametrized by supernatural numbers. The conjugacy classes and normal structure of each group of this class are characterized.
Keywords	class of groups, almost periodic permutations, parametrized by supernatural numbers, conjugacy classes
DOI	doi:10.30970/ms.19.2.115-126
Reference	1. Вершик А. М. Описание инвариантных мер для действий некоторых бесконечных групп. // Докл. АН СССР. – 1974. –Т. 218, № 4. – С. 749 – 752. 2. Залесский А.Е. Групповые кольца индуктивных пределов знакопеременных групп // Алгебра и анализ. –1990. – Т.2, № 6 –С.132–149. 3. Крошко Н.В., Сущанський В.I. Однорiдно симетричнi групи // Доп. НАН України. – 1993. – № 12. – С. 9–13. 4. Kroshko N.V., Sushchansky V.I. Direct limits of symmetric and alternating groups with strictly diagonal embeddings // Archiv der Mathematik. – 1998. –V.71. – P.173–182. 5. Gschwend T., Kegel O. H. On the group of weak automorphisms of a family of equivalence relations // Algebra and operator theory.– 1997.– P.237–248. 6. Brawley J. V., Schnibben G. E. Infinite algebraic extensions of finite fields.– Contemporary mathematics, Vol. 95.– Providence, Rhode Island:–Amer. Math. Soc. – 1992.– 104 p. 7. Назарчук В.В., Сущанський В.I. Групи перiодично визначених пiдстановок. // Доп. НАН України. – 2003. – № 3.– С.26–30. 8. Bhattacharjee M., Macpherson D., Möller R.G., Neumann P. Notes on Infinite Permutation Groups. – New Delhi: Hindustan Book Agency.– 1997. – 202 p.
Pages	115-126
Volume	19
Issue	2
Year	2003
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Groups of periodically defined permutations on a countable set (in Russian)