Abstract
Given a subgroup A of a group G and some group-theoretic property θ of subgroups, say that A enjoys the gradewise property θ in G whenever G has a normal series
such that for each i = 1, …, t the subgroup (A ∩ G i )G i−1/G i−1 enjoys the property θ in G/G i−1. Basing on this concept, we obtain a new characterization of finite supersolvable and solvable groups.
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Original Russian Text Copyright © 2015 Guo W. and Skiba A.N.
The first author was supported by the NNSF of China (Grant 11371335) and the Wu Wen-Tsun Key Laboratory of Mathematics, USTC, the Chinese Academy of Sciences. The second author was supported by the Chinese Academy of Sciences Visiting Professorship for Senior International Scientists (Grant 2010T2J12).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 3, pp. 487–497, May–June, 2015; DOI: 10.17377/smzh.2015.56.302.
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Guo, W., Skiba, A.N. Gradewise properties of subgroups of finite groups. Sib Math J 56, 384–392 (2015). https://doi.org/10.1134/S0037446615030027
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DOI: https://doi.org/10.1134/S0037446615030027