C-Supplemented subgroups of finite groups

By A. Ballester-Bolinches, Yanming Wang, Xiuyun Guo. Glasgow Mathematical Journal, 2000

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On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups (2010, methodology): “Recall that a subgroup A of a group G is said to be S-quasinormal, S-permutable, or pðGÞ-permutable in G (Kegel [17]) if AP 1⁄4 PA for all Sylow subgroups P of G; the subgroup A is said to be c-normal in G (Wang [26]) if G has a normal subgroup T such that AT 1⁄4 G and AVT cAG; and A is said to be c”
On Some Results in the Theory of Finite Partially Soluble Groups (2016, background): “Note also that if H is either complemented in G or normal in G, then H satisfies the following (Ballester-Bolinches-Guo-Wang) condition: G has a subgroup M and a normal subgroup N such that HM = G and H ∩ M ≤ N ≤ H [7,80].”
On the ℱϕ-Hypercentre of Finite Groups (2014, background): “Guo ([2, 15]) introduced the concept of a c-supplemented subgroup and proved that G is soluble if and only if every Sylow subgroup of G is c-supplemented in G.”
A generalisation of Kramer's theorem and its applications (2002, background): “But examples in [1] showed that the converses are not true.”
On c-supplemented maximal and minimal subgroups of Sylow subgroups of finite groups (2004, background): “Wang, BallesterBolinches and Guo in 2000 introduced the concept of c-supplementation of a finite group which is weaker than both c-normality and complementation [10], [11] and generalized the above two results as applications.”