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Joins of Almost Subnormal Subgroups

Published online by Cambridge University Press:  20 January 2009

John C. Lennox
John C. Lennox
Affiliation:
University College, Cardiff, U.K.
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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
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 1 , February 1979 , pp. 33 - 34
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), 221–231.CrossRefGoogle Scholar
(2) Robinson, D. J. S., Joins of subnormal subgroups, Illinois J. Math. 9 (1965), 144–168.CrossRefGoogle Scholar
(3) Roseblade, J. E. and Stonehewer, S. E., Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423–435.CrossRefGoogle Scholar