Abstract
Let a finite group \(G=AB\) be the mutually permutable product of two p-soluble subgroups A and B for some prime p. We give a bound of the p-length of G from the p-lengths of A and B.
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A. Ballester-Bolinches, John Cossey, and M.C. Pedraza-Aguilera, On the exponent of mutually permutable products of two abelian groups, J. Algebra 466 (2016), 34-43.
A. Ballester-Bolinches, R. Esteban-Romero, and M. Asaad, Products of Finite Groups, Walter de Gruyter, Berlin–New York, 2010.
N. Itô, Über das Produkt von zwei abelschen Gruppen, Math. Z. 62 (1955), 400-401.
B. Huppert, Endliche Gruppen, Springer, Berlin–Heidelberg–New York, 1967.
B. Huppert and N. Blackburn, Finite groups II, Springer-Verlag, Berlin–Heidelberg–New York, 1982.
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Cossey, J., Li, Y. On the \({{\varvec{p}}}\)-length of the mutually permutable product of two \({{\varvec{p}}}\)-soluble groups. Arch. Math. 110, 533–537 (2018). https://doi.org/10.1007/s00013-018-1150-8
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DOI: https://doi.org/10.1007/s00013-018-1150-8