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. 
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47 Citations

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  • Mathematics
    Journal of the Australian Mathematical Society
  • 2001
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References

SHOWING 1-10 OF 12 REFERENCES

The embedding of quasinormal subgroups in finite groups

A subgroup of a group G is called quasinormal in G if it permutes with every subgroup of G. For a finite group G it is well known that quasinormal subgroups are not far from being normal: It6 and…

Finite groups with pro-normal subgroups

The purpose of this paper is to study a class of finite groups whose subgroups of prime power order are all pro-normal. Following P. Hall, we say that a subgroup H of a group G is pro-normal in G if…

A Course in the Theory of Groups

This is a detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the…

Subgroup Lattices of Groups

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large…

Über die endlichen Gruppen und die Verbände ihrer Untergruppen = 有限群トソノ部分群ノ束ニ就イテ

gruppi risolubili finiti in cui i sottogruppi di composizione coincidono con i sottogruppi quasi-normali

  • Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 37, No
  • 1964

A note on finite groups in which normality is transitive

Zur Sylowstruktur auflösbarer Gruppen

Contributions to the theory of groups of finite order

Zur Sylowstruktur auflösbarer Gruppen. II