Guo, Xiuyun; Shum, K. P. On \(c\)-normal maximal and minimal subgroups of Sylow \(p\)-subgroups of finite groups. (English) Zbl 1050.20010 Arch. Math. 80, No. 6, 561-569 (2003). A subgroup \(H\) of a finite group \(G\) is said to be \(c\)-normal in \(G\) if there exists a subgroup \(N\) of \(G\) such that \(G=HN\) and \(H\cap N\) is contained in \(\text{Core}_G(H)\), the largest normal subgroup of \(G\) contained in \(H\). For a prime \(p\), the authors study the influence of the \(c\)-normality of the maximal subgroups of the Sylow \(p\)-subgroups of a group and the \(c\)-normality of some minimal subgroups on the structure of a group. They find some criteria for a finite group \(G\) to be \(p\)-nilpotent, \(p\)-supersoluble, or to belong to a saturated formation. Reviewer: Adolfo Ballester-Bolinches (Burjasot) Cited in 2 ReviewsCited in 52 Documents MSC: 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D40 Products of subgroups of abstract finite groups Keywords:finite groups; maximal subgroups; Sylow subgroups PDFBibTeX XMLCite \textit{X. Guo} and \textit{K. P. Shum}, Arch. Math. 80, No. 6, 561--569 (2003; Zbl 1050.20010) Full Text: DOI