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We discuss a condition on a p-subgroup H of a finite group G that is both more general and easier to work with than the assumption that H is weakly s-permutable in G. Our condition is that $${U \cap H \triangleleft U}$$ U ∩ H ◃ U , where U = Op(H), and we assume that this condition holds for every subgroup H of order d that is normal in some fixed Sylow p-subgroup P of G, where d > ...
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