Abstract
A subgroup H of a finite group G is said to be Hall subnormally (respectively normally) embedded in G if there is a subnormal (respectively normal) subgroup N of G such that H is a Hall subgroup of N. The aim of this paper is to characterise the groups G having a Hall subnormally embedded subgroup of order |B| for each subgroup B of G. Some earlier results are consequences of our main theorem.
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Acknowledgments
The first author was supported by Proyecto MTM2014-54707-C3-1-P from Ministerio de Economía y Competitividad, Spain, and by Project from the National Natural Science Foundation of China (NSFC, No. 11271085). The third author was supported by Project from the National Natural Science Foundation of China (NSFC, No. 11201082), Cultivation Program for Outstanding Young College Teachers (Yq2013061) of Guangdong Province and Pei Ying Yu Cai Project of GDUT.
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Communicated by J. S. Wilson.
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Ballester-Bolinches, A., Cossey, J. & Qiao, S. On hall subnormally embedded subgroups of finite groups. Monatsh Math 181, 753–760 (2016). https://doi.org/10.1007/s00605-015-0838-0
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DOI: https://doi.org/10.1007/s00605-015-0838-0