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A note on the supersolubility of a group with ms-supersoluble factors

Abstract

A subgroup A of a group G is called seminormal in G, if there exists a subgroup B such that \(G=AB\) and AX is a subgroup of G for every subgroup X of B. Let G be a supersoluble group. Then it has an ordered Sylow tower of supersoluble type \(1=G_0< G_1< \cdots < G_m=G\). If for every i all maximal subgroups of \(G_{i}/G_{i-1}\) are seminormal in \(G/G_{i-1}\), then G is said to be ms-supersoluble. In this paper, we proved the supersolubility of a group \(G=AB\) under condition that A and B are normal in G and ms-supersoluble.

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Correspondence to Alexander Trofimuk.

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Trofimuk, A. A note on the supersolubility of a group with ms-supersoluble factors. Ricerche mat (2020). https://doi.org/10.1007/s11587-020-00493-w

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Keywords

  • Supersoluble group
  • Normal subgroup
  • Seminormal subgroup
  • ms-supersoluble group

Mathematics Subject Classification

  • 20D10
  • 20D20