On finite T-groups and the Wielandt subgroup

Gil Kaplan
2011 Journal of group theroy  
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
more » ... we provide new characterizations for finite solvable T-groups in Theorem 7.
doi:10.1515/jgt.2011.082 fatcat:dr2gnuwywvcdbponvwduqfoxya