On <Emphasis Type="Italic">G</Emphasis>-covering subgroup systems of finite groups |
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Authors: | Wenbin Guo Alexander N Skiba |
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Institution: | 1.Department of Mathematics,University of Science and Technology of China,Hefei,P. R. China;2.Department of Mathematics,Xuzhou Normal University,Xuzhou,P. R. China;3.Department of Mathematics,Francisk Skorina Gomel State University,Gomel,Belarus |
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Abstract: | Let \(\mathcal{F}\) be a class of groups and G a finite group. We call a set Σ of subgroups of G a G-covering subgroup system for \(\mathcal{F}\) if \(G\in \mathcal{F}\) whenever \(\Sigma \subseteq \mathcal{F}\). Let p be any prime dividing |G| and P a Sylow p-subgroup of G. Then we write Σ p to denote the set of subgroups of G which contains at least one supplement to G of each maximal subgroup of P. We prove that the sets Σ p and Σ p ∪Σ q , where q≠p, are G-covering subgroup systems for many classes of finite groups. |
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