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Siberian Mathematical Journal

, Volume 56, Issue 3, pp 384–392 | Cite as

Gradewise properties of subgroups of finite groups

  • W. GuoEmail author
  • A. N. Skiba
Article

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
$$1 = G_0 \leqslant G_1 \leqslant \cdots \leqslant G_t = G$$
such that for each i = 1, …, t the subgroup (AG 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.

Keywords

finite group subgroup functor gradewise property solvable group supersolvable group 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.School of Mathematical ScienceUniversity of Science and Technology of ChinaHefeiP. R. China
  2. 2.Skorina Gomel State UniversityGomelBelarus

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