Abstract
Let G be a finite group and \({\mathcal{F}}\) a formation of finite groups. We say that a subgroup H of G is \({\mathcal{F}}\) -supplemented in G if there exists a subgroup T of G such that G = TH and \({(H\cap T)H_{G}/H_{G}}\) is contained in the \({\mathcal{F}}\) -hypercenter \(Z_{\infty}^{\mathcal F}(G/H_{G})\) of G/H G . In this paper, we use \({{\mathcal F}}\) -supplemented subgroups to study the structure of finite groups. A series of previously known results are unified and generalized.
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Research of the author is supported by a NNSF grant of China (Grant #10771180).
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Guo, W. On \({\mathcal{F}}\) -supplemented subgroups of finite groups. manuscripta math. 127, 139–150 (2008). https://doi.org/10.1007/s00229-008-0194-7
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DOI: https://doi.org/10.1007/s00229-008-0194-7