Author, Subjects, Keywords

Cited Author

» By Author or Editor
» Browse Author by Alphabet
» By Journal
» By Subjects
» Malaysian Journals
» By Type
» By Year

» By Author
» Top 20 Authors
» Top 20 Article
» Top Journal Cited
» Top Article Cited
» Journal Citation Statistics
» Usage Since Sept 2007

# On a Class of Residually Finite Groups

Taeri, B., (2003) On a Class of Residually Finite Groups. Bulletin of the Malaysian Mathematical Sciences Society, 26 (2). pp. 209-219. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v26n2/v26n2p7.pdf

## Affiliations

Isfahan University of Technology, Dept. of Mathematics

## Abstract

Let , be positive integers and be non-zero integers. We denote by the class of groups in which, for every subset of of cardinality , there exist a subset , with ,, and a function , with such that [,,...,] where , . The class is defined exactly as , with additional conditions " whenever , where “.

Let be a finitely generated residually finite group. Here we prove that

(1) If , then has a normal nilpotent subgroup with finite index such that the nilpotency class of , is bounded by a function of , where , is the torsion subgroup of .

(2) If be generated, then has a normal nilpotent subgroup whose index and the nilpotency class are bounded by a function of .

Item Type: Journal Q Science, Computer Science 1195

1. A. Abdollahi, Some Engel conditions on infinite subsets of certain groups, Bull. Austral. Math. Soc. 62 (2000), 141—148.

2. A. Abdollahi, Some Engel conditions on finite subsets of certain groups, Houston J. Math. 27 (2001), 511—522.

3. Abdollahi and Taeri, B. A condition on finitely generated soluble groups, Comm. Algebra 27 (1999), 5633—5638.

4. Abdollahi and Taeri, B. A condition on certain variety of groups, Rend. Sem. Mat. Univ. Padova 104(2000), 129—134.

5. Abdollahi and Taeri, B. Some conditions on infinite subsets of infinite groups, Bull. Malaysian Math. Soc. 22 (1999), 1—7.

6. Abdollahi and Taeri, B. On a class of infinite rings, Algebra Colloq. 8:2, (2001), 153—157.

7. C. Delizia, A. Rhamtulla and H. Smith, Locally graded groups with a nilpotency condition on infinite subsets, J. Austral. Math. Soc. (series A) 69(2000), 415—420.

8. G. Endimioni, Groups covered by finitely many nilpotent subgroup , Bull. Austral Math. Soc. 50(1994), 459—464.

9. G. Endimioni, Groupes finis satisfaisant la condition (N,n), C. R. Acad. Sci. Paris, 1. 319 Serie I, (1994), 1245—1247.

10. G. Endimioni, On a combinatorial problem in varieties of groups, Comm. Algebra 14:23 (1995) 5297—5307.

11. J.C. Lennox and J. Wiegold, Extension of a problem of Paul Erdos on groups, J. Austral. Math. Soc. (series A) 31 (1981) 451—463.

12. P. Longobardi and M. Maj, Finitely generated soluble groups with an Engel condition on infinite subsets, Rend. Sem. Mat. Univ. Padova 89 (1993), 97—102.

13. P. Longobardi, M. Maj and A. Rhemtulla, Infinite group in a given variety and Ramsey’s Theorem, Comm. Algebra 20 (1992), 127—139.

14. P. Longobardi, M. Maj and A. Rhemtulla, Groups with no free subsemigroups, Trans. Amer. Math. Soc. 374:4 (1995), 1419—1427.

15. B.H. Neumann, Twisted wreath products of groups, Arch. Math. (Base]) 123 (1963), 1—6.

16. B.H. Neumann, A problem of Paul Erdos on groups, J. Austral. Math. Soc. (Series A) 21(1976), 467—472.

17. D.J.S. Robinson, A Course in the Theory of Groups, 2nd. ed., Springer-Verlag, Berlin, 1996.

18. J.F. Semple and A. Shalev, Combinatorial conditions in residually finite groups I, J. Algebra 157 (1993), 43—50.

19. Shalev, Combinatorial conditions in residually finite groups II, J. Algebra 157 (1993), 51—62.

20. Taeri, B. A combinatorial condition on a certain variety of groups, Arch. Math. (Basel) 77 (2001), 456—460.

21. Taeri, B. A question of Paul Erdos and nilpotent-by-finite groups, Bull. Austral. Math. Soc. 64 (2001), 245—254.

22. Taeri, B. On a combinatorial problem in group theory, To appear in Southeast Asian Math. Bull.

23. N. Trabelsi, Characterisation of nilpotent-by-finite groups, Bull. Austral. Math. Soc. 61(2000), 33—38.

24. J.S. Wilson, Two generator condition in residually finite groups, Bull. London Math. Soc. 23 (1991), 239—248.

25. E.I. Zel’manov, On some problems of group theory and Lie algebras, Math. Sb. 180 (1989), 159—167.

26. E.I. Zel’manov, Solution of the restricted Burnside problem for groups of odd exponent, Izv. Akad. Nauk SSSR ser. Mat. 54 (1990), 42—59.

27. E.I. Zel’manov, Solution of the restricted Burnside problem for 2-groups, Math. SSSR-Sb. 182 (1991), 568—592.

Repository Staff Only: item control page