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Hypercentral injectors in infinite soluble groups

Published online by Cambridge University Press:  20 January 2009

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
University of Glasgow
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The Carter subgroups of a finite soluble group may be characterised either as theself-normalising nilpotent subgroups or as the nilpotent projectors. Subgroups with properties analogous to both of these have been considered by Newell (2, 3) in the class of -groups. The results obtained are necessarily less satisfactory than in the finite case, the subgroups either being almost self-normalising (i.e. having finite index in their normaliser) or having an almost-covering property. Also the subgroups are not necessarily conjugate but lie in finitely many conjugacy classes.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 191 - 194
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Huppert, B., Endliche Gruppen I (Grundlehren der math. Wiss. 134, Springer, 1967).CrossRefGoogle Scholar
(2) Newell, M. L., Supplements in abelian-by-nilpotent groups, J. London Math. Soc. (2), 11 (1975), 74–80.CrossRefGoogle Scholar
(3) Newell, M. L., Nilpotent projectors in 1groups, Proc. Royal Irish Acad. (Section A) 75 (1975), 107–114.Google Scholar
(4) Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Ergebnisse der Math. 62, 63, Springer, 1972).Google Scholar