Abstract
Let ℱ 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 ℱ (or, in other words, an ℱ-covering system of subgroups in G) if G ∈ ℱ wherever either Σ = ∅ or Σ ≠ ∅ and every subgroup in Σ belongs to ℱ. 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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Original Russian Text Copyright © 2006 Li Y.
The author was partially supported by the NSF of China (Grant 10571181), the NSF of the Guangdong Province (Grant 04300023) and Guangdong Institutions of Higher Learning, College and University (Grant Z03095) and ARF (GDEI).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 575–583, May–June, 2006.
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Li, Y. G-covering systems of subgroups for the class of supersoluble groups. Sib Math J 47, 474–480 (2006). https://doi.org/10.1007/s11202-006-0059-9
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DOI: https://doi.org/10.1007/s11202-006-0059-9