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Group theoretic properties inherited by lower central factors

Published online by Cambridge University Press:  18 May 2009

Howard Smith
Howard Smith
Affiliation:
Mathematics Institute University College, Cardiff Wales.
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Several properties are known to be inherited from the derived factor group of a group G by other factors Γi = γi(G)/γi + 1(G) of the lower central series. Derek Robinson proved [1] that the denning property of any class of groups which is closed under the forming of homomorphic images of tensor products is so inherited. Possibilities for here include the following classes.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 89 - 91
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Robinson, D. J. S., A property of the lower central series of a group, Math. Z. 107 (1968), 225–231.CrossRefGoogle Scholar
2.Smith, H., Hypercentral groups with all subgroups subnormal II, Bull. London Math. Soc. 18 (1986) 343–348.Google Scholar
3.Williams, J. P., The join of several subnormal subgroups, Math. Proc. Cambridge Philos. Soc. 92 (1982), 391–399.CrossRefGoogle Scholar