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NILPOTENCY IN UNCOUNTABLE GROUPS

  • FRANCESCO DE GIOVANNI (a1) and MARCO TROMBETTI (a2)

Abstract

The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}$ or the generalized continuum hypothesis is assumed to hold. Furthermore, groups whose proper subgroups of large cardinality are soluble are studied in the last part of the paper.

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The authors are members of GNSAGA-INdAM, and this work was carried out within the ADV-AGTA project.

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References

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