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Finite groups with \(\mathbb{P }\)-subnormal subgroups

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Abstract

A subgroup \(H\) of a group \(G\) is called \(\mathbb{P }\)-subnormal in \(G\) whenever either \(H=G\) or there is a chain of subgroups \(H=H_0\subset H_1\subset \cdots \subset H_n=G\) such that \(|H_i:H_{i-1}|\) is a prime for all \(i\). In this paper we study groups with \(\mathbb{P }\)-subnormal 2-maximal subgroups, and groups with \(\mathbb{P }\)-subnormal primary cyclic subgroups.

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Acknowledgments

We would like to thank A. F. Vasilyev for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics Gomel F. Scorina State University, Sovetskaya Str. 104, Gomel, 246019, Belarus

    Victor S. Monakhov

  2. Gomel Engineering Institute of MES of Belarus, Retchitskoe Shosse 35a, Gomel, 246035, Belarus

    Viktoryia N. Kniahina

Authors
  1. Victor S. Monakhov
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  2. Viktoryia N. Kniahina
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Correspondence to Viktoryia N. Kniahina.

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Communicated by F. de Giovanni.

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Monakhov, V.S., Kniahina, V.N. Finite groups with \(\mathbb{P }\)-subnormal subgroups. Ricerche mat. 62, 307–322 (2013). https://doi.org/10.1007/s11587-013-0153-9

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  • DOI: https://doi.org/10.1007/s11587-013-0153-9

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