On \(S\)-permutably embedded subgroups of finite groups
A subgroup \(A\) of a finite group \(G\) is said to be \(S\)-permutably embedded in \(G\) if for each prime \(p\) dividing the order of \(A\), every Sylow \(p\)-subgroup of \(A\) is a Sylow \(p\)-subgroup of some \(S\)-permutable subgroup of \(G\). In this paper we determine how the \(S\)-permutable embedding of several families of subgroups of a finite group influences its structure.
KeywordsFinite group Permutability \(S\)-permutability Maximal subgroups Minimal subgroups
Mathematics Subject Classification (2000)20D05 20D10 20D35 20F17
The first author was supported by the Ministerio de Ciencia e Innovación of Spain (Grant MTM2010-19938-C03-01), and the second author was supported by the National Natural Science Foundation of China (Grant No. 11171353/A010201) and the Natural Science Foundation of Guangdong Province (S2011010004447). Both authors were also supported by Project of NSFC (11271085).
- 7.Ezquerro, L.M.: On subnormally embedded subgroups of finite groups. In: Ballester-Bolinches, A., Elduque, A., Muñoz-Escolano, J.M. (eds.) Proceedings of the “Meeting on Group Theory and Applications on the occasion of Javier Otal’s 60th birthday” (Zaragoza, June 10–11, 2011), Biblioteca de la Revista Matemática Iberoamericana, pp. 127–149. Real Sociedad Matemática Española, Madrid (2012)Google Scholar
- 10.Li, Y.: Finite groups with some S-permutable subgroups. (Submitted)Google Scholar