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- Title
Permutable subnormal subgroups of finite groups.
- Authors
A. Ballester-Bolinches; J. Beidleman; John Cossey; R. Esteban-Romero; M. Ragland; Jack Schmidt
- Abstract
Abstract.  The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called $${\mathcal{PT}}$$-groups. In particular, it is shown that the finite solvable $${\mathcal{PT}}$$-groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is permutable sensitive. However, there exist finite insolvable groups which are not $${\mathcal{PT}}$$-groups but all subnormal subgroups of defect two are permutable.
- Subjects
PERMUTATION groups; FINITE groups; MULTIPLY transitive groups; SOLVABLE groups; DEVIATION (Statistics); MODULAR groups; COINCIDENCE theory; MATHEMATICAL proofs
- Publication
Archiv der Mathematik, 2009, Vol 92, Issue 6, p549
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-009-2976-x