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A Property of Groups with No Central Factors

Published online by Cambridge University Press:  20 November 2018

A. H. Rhemtulla
A. H. Rhemtulla*
Affiliation:
The University of Alberta Edmonton, Alberta
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Let C1 denote the class of all groups with no non-trivial central factors. We prove the following theorem

There exist non-trivial locally solvable C1 groups; but there is no non-trivial locally k-step polynilpotent C1 group for any integer k.

It is well known that a minimal normal subgroup of a locally solvable group is abelian. Thus no non-trivial locally solvable group can be pluperfect - the class of all perfect groups in which every subnormal subgroup is also perfect.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 467 - 470
Copyright
Copyright © Canadian Mathematical Society 1969

References

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