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On the Wielandt subgroup of infinite soluble groups

Published online by Cambridge University Press:  18 May 2009

Rolf Brandl ,
Silvana Franciosi  and
Francesco de Giovanni
Rolf Brandl
Affiliation:
Mathematisches InstitutUniversität WurzburgAm Hubland 12D-8700 WürzburgWest Germany
Silvana Franciosi
Affiliation:
Istituto di Matematica Facoltà di ScienzeUniversitá di Salerno1–84100 Salerno, Italy
Francesco de Giovanni
Affiliation:
Dipartimento di MatematicaUniversità di NapoliVia Mezzocannone 81–0134 Napoli, Italy
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The Wielandt subgroup w(G) of a group G is defined to be the intersection of the normalizers of all the subnormal subgroups of G. If G is a group satisfying the minimal condition on subnormal subgroups then Wielandt [10] showed that w(G) contains every minimal normal subgroup of G, and so contains the socle of G, and, later, Robinson [6] and Roseblade [9] proved that w(G) has finite index in G.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 121 - 125
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

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