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Finite factorizable groups with solvable ℙ2-subnormal subgroups

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Abstract

A subgroup H of a finite group G is called ℙ2-subnormal whenever there exists a subgroup chain H = H 0 ≤ H 1 ≤ ... ≤ H n = G such that |H i+1: H i | divides prime squares for all i. We study a finite group G = AB on assuming that A and B are solvable subgroups and the indices of subgroups in the chains joining A and B with the group divide prime squares. In particular, we prove that a group of this type is solvable without using the classification of finite simple groups.

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Authors and Affiliations

  1. Gomel Engineering Institute, Gomel, Belarus

    V. N. Kniahina

  2. Francisk Skorina Gomel State University, Gomel, Belarus

    V. S. Monakhov

Authors
  1. V. N. Kniahina
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  2. V. S. Monakhov
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Corresponding author

Correspondence to V. N. Kniahina.

Additional information

To V. D. Mazurov on the occasion of his 70th birthday.

Original Russian Text Copyright © 2013 Kniahina V.N. and Monakhov V.S.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 1, pp. 77–85, January–February, 2013.

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Kniahina, V.N., Monakhov, V.S. Finite factorizable groups with solvable ℙ2-subnormal subgroups. Sib Math J 54, 56–63 (2013). https://doi.org/10.1134/S0037446613010084

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  • DOI: https://doi.org/10.1134/S0037446613010084

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