Product of nilpotent subgroups |
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Authors: | MJ Iranzo J Medina F Pérez-Monasor |
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Institution: | Departament d'Algebra, Facultat de Matemátiques, Universitat de València, 46100 Burjassot. València, Spain, ES
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Abstract: | We will say that a subgroup X of G satisfies property C in G if CG(X?Xg)\leqq X?Xg{\rm C}_{G}(X\cap X^{{g}})\leqq X\cap X^{{g}} for all g ? G{g}\in G. We obtain that if X is a nilpotent subgroup satisfying property C in G, then XF(G) is nilpotent. As consequence it follows that if N\triangleleft GN\triangleleft G is nilpotent and X is a nilpotent subgroup of G then CG(N?X)\leqq XC_G(N\cap X)\leqq X implies that NX is nilpotent.¶We investigate the relationship between the maximal nilpotent subgroups satisfying property C and the nilpotent injectors in a finite group. |
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