Fan, Yun; Guo, Xiuyun; Shum, K. P. Remarks on two generalizations of normality of subgroups. (Chinese. English summary) Zbl 1109.20017 Chin. Ann. Math., Ser. A 27, No. 2, 169-176 (2006). Summary: A subgroup \(H\) is said to be semi cover-avoiding in a group \(G\) if there is a chief series \(1=G_0<G_1<\cdots<G_l=G\) such that for every \(j=1,\cdots,l\), either \(H\) covers \(G_j/G_{j-1}\) or \(H\) avoids \(G_j/G_{j-1}\). This paper shows that semi cover-avoidence is suitable to cover both \(C\)-normality and the cover-avoidence property, and to characterize the solvability of groups by means of maximal subgroups or Sylow subgroups. Cited in 2 ReviewsCited in 22 Documents MSC: 20D30 Series and lattices of subgroups 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D35 Subnormal subgroups of abstract finite groups 20E28 Maximal subgroups Keywords:maximal subgroups; chief series; semi-cover-avoiding property; finite groups; semi-cover-avoiding subgroups; solubility; supersolubility PDFBibTeX XMLCite \textit{Y. Fan} et al., Chin. Ann. Math., Ser. A 27, No. 2, 169--176 (2006; Zbl 1109.20017)