The Wielandt subgroup, the intersection of normalizers of subnormal subgroups, is
non-trivial in any finite group and thus gives rise to a series whose length is a measure
of the complexity of a group's subnormal structure. Another measure, akin to the
nilpotency class of nilpotent groups, arises from the strong Wielandt subgroup, the
intersection of centralizers of nilpotent subnormal sections. This thesis begins an
investigation into how these two invariants relate in finite soluble groups.
ΒΆ
Complete results are obtained for metabelian groups of odd order: the strong
Wielandt length of such a group is at most one more than its Wielandt length, and
this bound is best possible. Some progress is made in the wider class of groups with
p-length 1 for all primes p. A conjecture for all finite soluble groups, which may be
regarded as a subnormal analogue of the embedding of the Kern, is also considered.
| Identifer | oai:union.ndltd.org:ADTP/216720 |
| Date | January 2001 |
| Creators | Wetherell, Chris, chrisw@wintermute.anu.edu.au |
| Publisher | The Australian National University. Faculty of Science |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.anu.edu.au/legal/copyright/copyrit.html), Copyright Chris Wetherell |
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