G-covering systems of subgroups for the class of supersoluble groups |
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Authors: | Y Li |
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Institution: | (1) Nanchang University, Nanchang, Jiangxi, China;(2) Guangdong Institute of Education, Guangzhou, China |
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Abstract: | Let ? be a class of groups. Given a group G, assign to G some set of its subgroups Σ = Σ(G). We say that Σ is a G-covering system of subgroups for ? (or, in other words, an ?-covering system of subgroups in G) if G ∈ ? wherever either Σ = ? or Σ ≠ ? and every subgroup in Σ belongs to ?. In this paper, we provide some nontrivial sets of subgroups of a finite group G which are G-covering subgroup systems for the class of supersoluble groups. These are the generalizations of some recent results, such as in 1–3]. |
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Keywords: | Sylow subgroup supplement supersoluble group covering system |
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