On mutually permutable products of finite groups

[EN] The main purpose of this paper is to study mutually permutable products G = AB in which the subgroups of prime order p and cyclic of order 4 (if p = 2) of the largest normal subgroup of G contained in A boolean AND B are well situated in G. Our results confirm once again the important role of the intersection of the factors in the structural study of mutually permutable products.The first author is supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The first and second authors are supported by Major Projects in Basic Research and Applied Research (Natural Science) of Guangdong Province (2017KZDXM058). The first and third authors are supported by Prometeo/2017/057 of Generalitat (Valencian Community, Spain). The second author is supported by Funds of Guangzhou Science and Technology (No: 201804010088). The fourth author is supported by the project of NSF China (11401597).Ballester-Bolinches, A.; Li, Y.; Pedraza Aguilera, MC.; Su, N. (2018). On mutually permutable products of finite groups. Rendiconti Lincei - Matematica e Applicazioni. 29(4):711-719. https://doi.org/10.4171/RLM/83071171929