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On finite T-groups and the Wielandt subgroup
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February 10, 2011
Abstract
The Wielandt subgroup of a group G is the intersection of the normalizers of all the subnormal subgroups of G. A T-group is a group in which all the subnormal subgroups are normal, or, equivalently, a group coinciding with its Wielandt subgroup. We investigate the Wielandt subgroup of finite solvable groups and, in particular, find new properties and characterizations (see Theorems 1, 2 and Corollaries 4, 6) for this subgroup in the case that G is metanilpotent. Furthermore, we provide new characterizations for finite solvable T-groups in Theorem 7.
Received: 2010-06-22
Revised: 2010-09-27
Published Online: 2011-02-10
Published in Print: 2011-November
© de Gruyter 2011
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Articles in the same Issue
- Remarks on chains of weakly closed subgroups
- Closed normal subgroups of free pro-S-groups of finite rank
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- The number of conjugacy classes in pattern groups is not a polynomial function
- On finite T-groups and the Wielandt subgroup
- A direct product coming from a particular set of character degrees
- Centralizers in Ã2 groups
- On centralizers of parabolic subgroups in Coxeter groups
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- Cylindric embeddings of Cayley graphs
- Compactifications of a representation variety
