Influence of permutizers of subgroups on the structure of finite groups

• Autores: Shouhong Qiao, Guohua Qian, Yanming Wang
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 10, 2008, págs. 2307-2313
• Idioma: inglés
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• Resumen

  • A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G in G, PG(M), is G. In this paper, we characterize the supersolubility of finite groups by using the maximal permutizer condition. We also get some results for when both G/N and N are supersoluble, which implies that G is supersoluble. Our results unify or generalize some known results.