Locally finite groups associated with of the Bratteli diagrams (in Ukrainian)

Ya.V.Lavrenyuk; V.I.Sushchansky

We associate a locally finite group with a Bratteli diagram in a natural way. The normal structure of such groups is studied. A criterion of simplicity is proved, examples of groups of such type are considered.

1. Burns R.G. A wreath tower construction of countably infinite, locally finite groups // Math. Zeitschr. -- 1968. -- B.105. -- S.367--386.

2. K.R.Davidson $C^*$-Algebras by example. -- Amer. Math. Soc., Providence, RI, 1996.

3. Delcroix St., Meierfrankenfeld U. Locally finite simple groups of $1$-type // J. Algebra. -- 2002. -- V.247, № 2. -- P.728--746.

4. Kegel O.H., Wehrfritz B.A.F. Locally finite groups. -- North-Holland, Amsterdam-London, 1973.

5. Lavrenyuk Ya., Nekrashevych V. On classification of inductive limits of direct products of alternating groups // J. London Math. Soc. -- 2007. -- V.75, № 1. -- P.146--162.

6. Leinen F., Puglisi O. Ideals in group algebras of simple locally finite groups of 1-type // Pacific J. of Math. -- 2002. -- V.207, № 2. -- P.433--445.

7. Leinen F., Puglisi O. Diagonal limits of of finite alternating groups: confined subgroups, ideals, and positive defined functions // Illinois J. Math. -- 2003. -- V.47, № 1/2. -- P.345--360.

8. Leinen F., Puglisi O. Some results concerning simple locally finite groups of 1-type // J. Algebra. -- 2005. -- V.287. -- P.32--51.

9. Meierfrankenfeld U. Non-finitary locally finite simple groups // in ‘‘Finite and Locally Finite Groups'' B. Hartley et al., Eds., Kluwer Academic, Dordrecht, 1995. -- P.189--212,

10. Сущанский В.И. Локально конечная простая группа Фибоначчи // Вопросы Алгебры. -- 1999. -- Т.14. -- C.107--114.

	Locally finite groups associated with of the Bratteli diagrams (in Ukrainian)
Author	Ya.V.Lavrenyuk, V.I.Sushchansky ylavrenyuk@.kiev.ua, Wital.Suszczanski@polsl.pl Taras Shevchenko National University of Kyiv; Silesian University of Technology, Institute of Mathematics
Abstract	We associate a locally finite group with a Bratteli diagram in a natural way. The normal structure of such groups is studied. A criterion of simplicity is proved, examples of groups of such type are considered.
Keywords	locally finite group, Bratteli diagram, normal structure
DOI	doi:10.30970/ms.31.1.3-11
Reference	1. Burns R.G. A wreath tower construction of countably infinite, locally finite groups // Math. Zeitschr. -- 1968. -- B.105. -- S.367--386. 2. K.R.Davidson $C^*$-Algebras by example. -- Amer. Math. Soc., Providence, RI, 1996. 3. Delcroix St., Meierfrankenfeld U. Locally finite simple groups of $1$-type // J. Algebra. -- 2002. -- V.247, № 2. -- P.728--746. 4. Kegel O.H., Wehrfritz B.A.F. Locally finite groups. -- North-Holland, Amsterdam-London, 1973. 5. Lavrenyuk Ya., Nekrashevych V. On classification of inductive limits of direct products of alternating groups // J. London Math. Soc. -- 2007. -- V.75, № 1. -- P.146--162. 6. Leinen F., Puglisi O. Ideals in group algebras of simple locally finite groups of 1-type // Pacific J. of Math. -- 2002. -- V.207, № 2. -- P.433--445. 7. Leinen F., Puglisi O. Diagonal limits of of finite alternating groups: confined subgroups, ideals, and positive defined functions // Illinois J. Math. -- 2003. -- V.47, № 1/2. -- P.345--360. 8. Leinen F., Puglisi O. Some results concerning simple locally finite groups of 1-type // J. Algebra. -- 2005. -- V.287. -- P.32--51. 9. Meierfrankenfeld U. Non-finitary locally finite simple groups // in ‘‘Finite and Locally Finite Groups'' B. Hartley et al., Eds., Kluwer Academic, Dordrecht, 1995. -- P.189--212, 10. Сущанский В.И. Локально конечная простая группа Фибоначчи // Вопросы Алгебры. -- 1999. -- Т.14. -- C.107--114.
Pages	3-11
Volume	31
Issue	1
Year	2009
Journal	Matematychni Studii
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