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Finite groups with normally embedded subgroups
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Zhencai Shen
Published/Copyright:
March 11, 2010
Abstract
A subgroup H of the finite group G is said to be quasinormally (resp. S-quasinormally) embedded in G if for every Sylow subgroup P of H, there is a quasinormal (resp. S-quasinormal) subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain quasinormally (resp. S-quasinormally) embedded subgroups of prime-power order are studied. For example, if a group G has a normal subgroup H such that G/H ∈ ℱ and such that for each Sylow subgroup P of H, every member in some ℳd(P) is quasinormally embedded in G, then G ∈ ℱ: here ℳd(P) is a set of maximal subgroups of P with intersection the Frattini subgroup.
Received: 2008-11-23
Revised: 2009-05-10
Published Online: 2010-03-11
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
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- Zeros of Brauer characters and the defect zero graph
- On the vanishing prime graph of solvable groups
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