Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-02T08:48:34.862Z Has data issue: false hasContentIssue false

Groups with restriction on their infinite subnormal subgroups

Published online by Cambridge University Press:  20 January 2009

Hermann Heineken
Affiliation:
Mathematisches Institut, Universität WürzburgFederal Republic of Germany
Rights & Permissions [Opens in a new window]

Extract

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 group G is called a Bn-group, if all its subnormal subgroups are of defect n. If all infinite subnormal subgroups of G have defect n, we say that G is an IBn group. DeGiovanni and Franciosi [2] have considered soluble IBn groups and characterized them.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.De Giovanni, F. and Franciosi, S., Groups in which every infinite subnormal subgroup is normal, J. Algebra 96 (1985), 566580.CrossRefGoogle Scholar
2.De Giovanni, F. and Franciosi, S., Groups with infinite subnormal subgroups of bounded defect, Boll. Un. Mat. Ital. D (6) 4 (1985), 4956.Google Scholar
3.Gaschütz, W., Gruppen, in denen das Normalteilersein transitiv ist, J. Reine. Angew. Math. 198 (1957), 8792.CrossRefGoogle Scholar
4.Kassens, U., Die Wielandtlänge endlicher Gruppen (Hausarbeit zur Lehramtsprüfung, F.U. Berlin, 1980).Google Scholar
5.Robinson, D. J. S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc. 60, (1964), 2138.CrossRefGoogle Scholar
6.Wielandt, H., Eine Verallgemeinerung der invarianten Untergruppen, Math. Z. 45 (1939), 209244.CrossRefGoogle Scholar