Abstract
We say that the subgroups G 1 and G 2 of a group G are mutually permutable if G 1 permutes with every subgroup of G 2 and G 2 permutes with every subgroup of G 1. Let G=G 1 G 2…G n be the product of its pairwise permutable subgroups G 1,G 2,…,G n such that the product G i G j is mutually permutable. We investigate the structure of the finite group G if special properties of the factors G 1,G 2,…,G n are known. Our results improve and extend some results of Asaad and Shaalan [1], Ezquerro and Soler-Escrivà [9] and Asaad and Monakhov [3].
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Heliel, A.A., Hijazi, R.A. On mutually permutable products of finite groups. Acta Math Hung 139, 344–353 (2013). https://doi.org/10.1007/s10474-012-0281-9
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DOI: https://doi.org/10.1007/s10474-012-0281-9