Abstract
Subgroups \(A\) and \(B\) of a finite group are said to be mutually permutable (respectively, M-permutable and \({{\mathrm{sn}}}\)-permutable) if \(A\) permutes with every subgroup (respectively, every maximal subgroup and every subnormal subgroup) of \(B\) and viceversa. If every subgroup of \(A\) permutes with every subgroup of \(B\), then the product is said to be totally permutable. These kinds of products have received much attention in the last twenty years. The aim of this paper is to analyse the behaviour of finite pairwise mutually permutable, mutually M-permutable, mutually \({{\mathrm{sn}}}\)-permutable and totally permutable products with respect to certain classes of groups including the supersoluble groups, widely supersoluble groups, and also the classes of \(PST\)-, \(PT\)- and \(T\)-groups.
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Acknowledgments
The authors gratefully acknowledge the financial support from the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) represented by Unit of Research Groups through the grant number (MG/31/01) for the group entitled “Abstract Algebra and its Applications”. The first and the second author have been supported by research projects MTM2010-19938-C03-01 and MTM2010-19938-C03-03, respectively, from the Ministerio de Ciencia e Innovación, Spain. The first author has also been supported by the National Natural Science Foundation of China (Grant No. 11271085).
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Communicated by Kar Ping Shum.
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Ballester-Bolinches, A., Ezquerro, L.M., Heliel, A.A. et al. Some Results on Products of Finite Groups. Bull. Malays. Math. Sci. Soc. 40, 1341–1351 (2017). https://doi.org/10.1007/s40840-015-0111-7
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DOI: https://doi.org/10.1007/s40840-015-0111-7