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FC-nilpotent and FC-soluble groups

Published online by Cambridge University Press:  24 October 2008

A. M. Duguid  and
D. H. McLain
A. M. Duguid
Affiliation:
PeterhouseCambridge
D. H. McLain
Affiliation:
PeterhouseCambridge
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Extract

Let an element of a group be called an FC element if it has only a finite number of conjugates in the group. Baer(1) and Neumann (8) have discussed groups in which every element is FC, and called them FC-groups. Both Abelian and finite groups are trivially FC-groups; Neumann has studied the properties common to FC-groups and Abelian groups, and Baer the properties common to FC-groups and finite groups. Baer has also shown that, for an arbitrary group G, the set H1 of all FC elements is a characteristic subgroup. Haimo (3) has defined the FC-chain of a group G by

Hi/Hi−1 is the subgroup of all FC elements in G/Hi−1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 391 - 398
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

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