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On the normal cores of certain subgroups of nilpotent groups

Published online by Cambridge University Press:  18 May 2009

Howard Smith
Howard Smith
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, U.S.A.
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Let G be a group and H a subgroup of finite index in G. Then of course H contains a G-invariant subgroup C such that G/C is finite. In attempting to establish results of a similar nature, where “finite” is replaced by, for example, “finitely generated”, one notices immediately that a quite differently stated hypothesis is required. One reasonable approach would be to consider subgroups H which are “f.g. embedded” in G—indeed, the notion of a polycyclic embedding was utilised by P. Hall in [1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 113 - 115
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Hall, P., Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436.Google Scholar
2.Hall, P., The Edmonton notes on nilpotent groups (QMC Mathematics Notes 1969).Google Scholar