Primitive subgroups and PST-groups
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Ballester-Bolinches, Adolfo; Beidleman, J.C.; Esteban Romero, Ramón
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Aquest document és un/a article, creat/da en: 2014
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All groups are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as its proper subgroup. He, Qiao and Wang [7] proved that every primitive subgroup of a group G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group. |
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