Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T11:48:24.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Basis normalizers and Carter subgroups in a class of locally finite groups

Published online by Cambridge University Press:  24 October 2008

C. J. Graddon  and
B. Hartley
C. J. Graddon
Affiliation:
Mathematics Institute, University of Warwick, Coventry
B. Hartley
Affiliation:
Mathematics Institute, University of Warwick, Coventry
Get access Rights & Permissions [Opens in a new window]

Extract

We shall be working throughout this paper in the class of locally finite groups introduced in (3) and further discussed in (5) and (6), and all groups appearing will be assumed to belong to this class. By definition, is the largest subgroupclosed class of locally finite groups satisfying the conditions:

U1. If G ε then G has a finite series

with locally nilpotent factors.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 189 - 198
Copyright
Copyright © Cambridge Philosophical Society 1972

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)Alperin, J. L.System normalizers and Carter subgroups. J. Algebra 1 (1964), 355–366.CrossRefGoogle Scholar
(2)Carter, R. W.Nilpotont self-normalizing subgroups and system normalizers. Proc. London Math. Soc. (3), 12 (1962), 535–563.CrossRefGoogle Scholar
(3)Gardiner, A. D., Hartley, B. and Tomkinson, M. J.Saturated formations and Sylow structure in locally finite groups. J. Algebra 17 (1971), 177–211.CrossRefGoogle Scholar
(4)Graddon, C. J.F-reducers in finite soluble groups. J. Algebra 18 (1971), 574–587.CrossRefGoogle Scholar
(5)Hartley, B.F-abnormal subgroups of certain locally finite groups. Proc. London Math. Soc. (3) 23 (1971), 128–158.CrossRefGoogle Scholar
(6)Hartley, B.Sylow subgroups of locally finite groups. Proc. London Math. Soc. (3) 23 (1971), 159–192.CrossRefGoogle Scholar
(7)Hartley, B.Serial subgroups of locally finite groups. Proc. Cambridge Philos. Soc. 71 (1971), 199–201.CrossRefGoogle Scholar
(8)Robinson, D. J. S.Infinite soluble and nilpotent groups (Queen Mary College Mathematics Notes, Queen Mary College, London, 1967).Google Scholar
(9)Stonehewer, S. E.Formations and a class of locally soluble groups. Proc. Cambridge Philos. Soc. 62 (1966), 613–635.CrossRefGoogle Scholar