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Ukrainian Mathematical Journal

, Volume 63, Issue 11, pp 1745–1755 | Cite as

Q-Permutable subgroups of finite groups

  • Z. Pu
  • L. MiaoEmail author
Article
  • 35 Downloads

A subgroup H of a group G is called Q-permutable in G if there exists a subgroup B of G such that (1) G = HB and (2) if H 1 is a maximal subgroup of H containing H QG , then H 1 B = BH 1 < G, where H QG is the largest permutable subgroup of G contained in H. In this paper, we prove the following statement: Let \( \mathcal{F} \) be a saturated formation containing \( \mathcal{U} \) and let G be a group with a normal subgroup H such that \( {{G} \left/ {H} \right.} \in \mathcal{F} \). If every maximal subgroup of every noncyclic Sylow subgroup of F*(H) having no supersolvable supplement in G is Q-permutable in G, then \( G \in \mathcal{F} \).

Keywords

Normal Subgroup Maximal Subgroup Sylow Subgroup Minimal Normal Subgroup Saturated Formation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHexi UniversityGansuChina
  2. 2.School of Mathematical SciencesYangzhou UniversityYangzhouChina

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