Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T11:56:18.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Subgroups in Integral Group Rings

Published online by Cambridge University Press:  20 November 2018

Michael A. Dokuchaev  and
Stanley O. Juriaans
Michael A. Dokuchaev
Affiliation:
Instituto de Matemática e Estatίstica, Universidade de São Paulo, Caixa Postal 66.281, 05389-970 São Paulo, Brazil e-mail: [email protected]
Stanley O. Juriaans
Affiliation:
Instituto de Matemática e Estatίstica, Universidade de São Paulo, Caixa Postal 66.281, 05389-970 São Paulo, Brazil e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A p-subgroup version of the conjecture of Zassenhaus is proved for some finite solvable groups including solvable groups in which any Sylow p-subgroup is either abelian or generalized quaternion, solvable Frobenius groups, nilpotent-by-nilpotent groups and solvable groups whose orders are not divisible by the fourth power of any prime.

Keywords

20C0516S3416U60group ringstorsion unitsunique trace property(p-ZC3)
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1170 - 1179
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Bovdi, A., Marciniak, Z. and Sehgal, S. K., Torsion Units in Infinite Group Rings, J. Number Theory 47(1994), 284–299.Google Scholar
2. Coxeterand, H. S. M., Moser, W. O. J., Generators and Relations for Discrete Groups, Springer-Verlag, Berlin, 1980.Google Scholar
3. Dokuchaev, M. A., Torsion units in integral group ring ofnilpotent metabelian groups, Comm. Algebra (2) 20(1992), 423–435.Google Scholar
4. Dokuchaev, M. A. and Sehgal, S. K., Torsion Units in Integral Group Rings of Solvable Groups, Comm. Algebra (12) 22(1994), 5005–5020.Google Scholar
5. Fernandes, N. A., Torsion Units in the Integral Group Ring of S4, Bol. Soc. Brasil. Mat. (1) 18(1987), 1–10.Google Scholar
6. Gorenstein, D., Finite groups, Harper & Row, New York, 1968.Google Scholar
7. Juriaans, S. O., Torsion units in integral group rings, Comm. Algebra (12) 22(1994), 4905–4913.Google Scholar
8. Juriaans, S. O., Torsion Units in Integral Group Rings II, Canad. Math. Bull, to appear.Google Scholar
9. Kimmerle, W. and Roggenkamp, K. W., Projective Limits of Group Rings, J. Pure Appl. Algebra 88(1993), 119–142.Google Scholar
10. Kimmerle, W., Roggenkamp, K. W. and Zimmerman, A., DMV-Seminar Part 1 Group Rings: Units and the Isomorphism Problem. Google Scholar
11. Klinger, L., Construction of a counterexample to a conjecture ofZassenhaus, Comm. Algebra 19(1993), 2303–2330.Google Scholar
12. Lichtman, A. I. and Sehgal, S. K., The elements of finite order in the group of units of group rings of free products of groups, Comm. Algebra 17(1989), 2223–2253.Google Scholar
13. Luthar, I. S. and Passi, I. B. S., Zassenhaus conjecture for A5, Proc. Indian Acad. Sci. (1) 99(1989), 1–5.Google Scholar
14. Marciniak, Z., Ritter, J., Sehgal, S. K. and Weiss, A., Torsion units in integral group rings of some metabelian groups, II, J. Number Theory 25(1987), 340–352.Google Scholar
15. Polcino Milies, C., Ritter, J. and Sehgal, S. K., On a conjecture ofZassenhaus on torsion units in integral group rings II, Proc. Amer. Math. Soc. (2) 97(1986), 206–210.Google Scholar
16. Polcino Milies, C. and Sehgal, S. K., Torsion Units in integral group rings of metacydie groups, J. Number Theory 19(1984), 103–114.Google Scholar
17. Passman, D. S., Permutation groups, W. A. Benjamin, Inc., New York, 1968.Google Scholar
18. Robinson, D. J. J., A course in the theory of groups, Springer-Verlag, New York, Heidelberg, Berlin, 1980.Google Scholar
19. Sehgal, S. K., Units of Integral Group Rings, Longman's, Essex, 1993.Google Scholar
20. Shirvani, M. and Wehrfritz, B. A. F., Skew Linear Groups, Cambridge, Univ. Press, 1986.Google Scholar
21. Valenti, A., Torsion Units in Integral Group Rings, Proc. Amer. Math. Soc. (1) 120(1994), 1—4.Google Scholar
22. Weiss, A., Torsion units in integral group rings, J. Reine Angew. Math. 415(1991), 175–187.Google Scholar