Huang, Qiong; Ma, Baiwan; Huang, Xinda; Wei, Huaquan; Yang, Liying Subnormal subgroups and \(p\)-super solvability of finite groups. (Chinese. English summary) Zbl 1363.20022 J. Chongqing Norm. Univ., Nat. Sci. 33, No. 1, 73-75 (2016). Summary: Assume that group a \(G\) has a solvable normal subgroup \(H\) and \(G/H\) is a \(p\)-super solvable group. We prove that: (1) If the maximal subgroup of Sylow \(p\)-subgroup \(P\) of \(H\) is subnormal in \(G\), then \(G\) is a \(p\)-super solvable group; (2) If the maximal subgroup of \(O_{p'}(H)\) is included in \(F_p(H)\) and is subnormal in \(G\), then \(G\) is a \(p\)-super solvable group. MSC: 20D35 Subnormal subgroups of abstract finite groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D15 Finite nilpotent groups, \(p\)-groups 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure Keywords:\(p\)-super solvable group; subnormal subgroup; Sylow \(p\)-subgroup PDFBibTeX XMLCite \textit{Q. Huang} et al., J. Chongqing Norm. Univ., Nat. Sci. 33, No. 1, 73--75 (2016; Zbl 1363.20022) Full Text: DOI