Hao, Chenggong; Wang, Xia; Chang, Xuewu Extension problems of morphisms in fusion systems. (Chinese. English summary) Zbl 1363.20016 J. North Univ. China, Nat. Sci. 36, No. 6, 614-616, 625 (2015). Summary: An exploration was made on some equivalent descriptions and basic properties of the domestic subgroups and essential subgroups of a fusion system. A characterization was presented on maximal Sylow intersections and domestic subgroups. Precisely, the following result is proved: Let \(F\) be a saturated fusion system on a finite \(p\)-group \(P\). A fully normalized subgroup \(Q\) is \(F\)-essential if and only if \(Q\) has a strong non-extendible \(F\)-automorphism; \(Q\) is a domestic subgroup if and only if \(Q\) has a non-extendible \(F\)-automorphism. MSC: 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20D15 Finite nilpotent groups, \(p\)-groups 20D45 Automorphisms of abstract finite groups 20D25 Special subgroups (Frattini, Fitting, etc.) 55R35 Classifying spaces of groups and \(H\)-spaces in algebraic topology Keywords:fusion system; Sylow intersection; domestic subgroup PDFBibTeX XMLCite \textit{C. Hao} et al., J. North Univ. China, Nat. Sci. 36, No. 6, 614--616, 625 (2015; Zbl 1363.20016) Full Text: DOI