# Criteria for Permutability to Be Transitive in Finite Groups

@article{Beidleman1999CriteriaFP, title={Criteria for Permutability to Be Transitive in Finite Groups}, author={J. Beidleman and Ben Brewster and Derek J. S. Robinson}, journal={Journal of Algebra}, year={1999}, volume={222}, pages={400-412} }

Abstract A group G is a PT - group if, for subgroups H and K with H permutable in K and K permutable in G , it is always the case that H is permutable in G . It is shown that a finite group is a soluble PT -group if and only if each subgroup of a Sylow subgroup is permutable in the Sylow normalizer.

## 47 Citations

### A note on finite groups in which c-permutability is transitive

- Mathematics
- 2012

A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=G and H∩P≦HpG, where HpG is the largest permutable subgroup of G contained in H. A group G is called…

### A note on finite groups in which c-permutability is transitive

- MathematicsActa Mathematica Hungarica
- 2011

A subgroup H of G is c-permutable in G if there exists a permutable subgroup P of G such that HP=G and H∩P≦HpG, where HpG is the largest permutable subgroup of G contained in H. A group G is called…

### Local characterizations of infinite groups whose ascendant subgroups are permutable

- Mathematics
- 2009

Abstract A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. Every permutable subgroup is ascendant, but, in general, the converse is far from being true.…

### Finite groups with transitive semipermutability

- Mathematics
- 2008

A group G is said to be a T-group (resp. PT-group, PST-group), if normality (resp. permutability, S-permutability) is a transitive relation. In this paper, we get the characterization of finite…

### Algorithms for permutability in finite groups

- Mathematics
- 2013

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is…

### The structure of finite groups in which permutability is a transitive relation

- MathematicsJournal of the Australian Mathematical Society
- 2001

Abstract The structure of finite groups in which permutability is transitive (PT-groups) is studied in detail. In particular a finite PT-group has simple chief factors and the p-chief factors fall…

### On Minimal Non PT-Groups

- Mathematics
- 2008

A finite group G is said to be a PT-group if every subnormal subgroup of G is permutable in G. In this paper, we determine the structure of a non PT-group all of its proper subgroups are PT-groups.…

### Finite groups in which normality, permutability or Sylow permutability is transitive

- Mathematics
- 2014

Abstract Y. Li gave a characterization of the class of finite soluble groups in which every subnormal subgroup is normal by means of NE-subgroups: a subgroup H of a group G is called an NE-subgroup…

### Finite groups in which permutability is a transitive relation on their frattini factor groups

- Mathematics
- 2007

Let G be a finite group. A PT-group is a group G whose subnormal subgroups are all permutable in G. A PST-group is a group G whose subnormal subgroups are all S-permutable in G. We say that G is a…

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