G-covering subgroup systems for the classes of supersoluble and nilpotent groups |
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| Authors: | Wenbin Guo K. P. Shum Alexander Skiba |
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| Affiliation: | (1) Department of Mathematics, Xuzhou Normal University, 221009 Xuzhou, P.R. China;(2) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, P. R. China;(3) Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China (SAR);(4) Department of Mathematics, Fr. Skaryna Gomel State University, 246019 Gomel, Belarus |
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| Abstract: | ![]()
LetF be a class of groups andG a group. We call a set Σ of subgroups ofG aG-covering subgroup system for the classF (or directly aF-covering subgroup system ofG) ifG ∈F whenever every subgroup in Σ is inF. In this paper, we provide some nontrivial sets of subgroups of a finite groupG which are simultaneouslyG-covering subgroup systems for the classes of supersoluble and nilpotent groups. Research of the first author is supported by the NNSF of China (Grant No. 10171086) and QLGCF of Jiangsu Province and a Croucher Fellowship of Hong Kong. Research of the second author is partially supported by a UGC (HK) grant #2060176 (2001/2002). |
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