Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T14:12:33.373Z Has data issue: false hasContentIssue false
  • English
  • Français

Groups whose irreducible representations have finite degree: III

Published online by Cambridge University Press:  24 October 2008

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

Extract

If F is a (commutative) field let XF denote the class of all groups G such that every irreducible FG module has finite dimension over F. In the first paper (9) of this series we classified finitely generated soluble XF-groups for each field F and in the second (10) we characterized soluble XF-groups for each field F of characteristic zero. Here we consider soluble XF-groups over fields F of positive characteristic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 397 - 406
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Fuchs, L.Infinite abelian groups, vol. 1 (Academic Press, New York, London 1970).Google Scholar
(2)Gruenberg, K. W.Cohomological topics in group theory. Springer Lecture Notes in Math. vol. 143 (Berlin, Heidelberg, New York, 1970).Google Scholar
(3)Hall, P.Periodic FC-groups. J. London Math. Soc. 34 (1959), 289–304.Google Scholar
(4)Jacobson, N.Lectures in abstract algebra, vol. 3 (American Book Co., New York, etc., 1964).Google Scholar
(5)Kegel, O. H. and Wehrfritz, B. A. F.Locally finite groups (North Holland Pub. Co., Amsterdam, London 1973).Google Scholar
(6)Passman, D. S.The algebraic structure of group rings (John Wiley, New York 1977).Google Scholar
(7)Robinson, D. J. S.Finiteness conditions and generalized soluble groups, vol. 2 (Springer, Berlin, Heidelberg, New York, 1972).Google Scholar
(8)Wehrfritz, B. A. F.Infinite linear groups (Springer, Berlin, Heidelberg, New York, 1973).Google Scholar
(9)Wehrfritz, B. A. F.Groups whose irreducible representations have finite degree. Math. Proc. Cambridge Phil. Soc. 90 (1981), 411–421.Google Scholar
(10)Wehrfritz, B. A. F.Groups whose irreducible representations have finite degree: II (submitted to Proc. Edinburgh Math. Soc.).Google Scholar