Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T05:38:45.594Z Has data issue: false hasContentIssue false

Joins of Almost Subnormal Subgroups

Published online by Cambridge University Press:  20 January 2009

John C. Lennox
Affiliation:
University College, Cardiff, U.K.
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.

Following (1) we say that a subgroup H of a group G is almost subnormal in G if H is of finite index in some subnormal subgroup of G, or, equivalently, if |Hn : H| is finite for some n, where Hn is the n-th term of the normal closure series of H in G. The aim of this article is to prove, in answer to a question of R. Baer, the following analogue of the well known result of Roseblade and Stonehewer (3) that in any group the join of a pair of finitely generated subnormal subgroups is always subnormal:

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Lennox, J. C., Groups in which every subgroup is almost subnormal, J. London Math. Soc. 15 (1977), 221231.CrossRefGoogle Scholar
(2) Robinson, D. J. S., Joins of subnormal subgroups, Illinois J. Math. 9 (1965), 144168.CrossRefGoogle Scholar
(3) Roseblade, J. E. and Stonehewer, S. E., Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423435.CrossRefGoogle Scholar