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


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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  1. 1.

    Huppert, B.: Endliche Gruppen I. Springer, Berlin (1967)

  2. 2.

    Monakhov, V.S.: Introduction to the Theory of Finite Groups and Their Classes. Vyshejshaja Shkola, Minsk (2006)

  3. 3.

    Robinson, D.: A Course in the Theory of Groups. Springer, Berlin (1988)

  4. 4.

    Huppert, B.: Monomialle darstellung endlicher gruppen. Nagoya Math. J. 3, 93–94 (1953)

  5. 5.

    Baer, R.: Classes of finite groups and their properties. Illinois J. Math. 1, 115–187 (1957)

  6. 6.

    Friesen, D.: Products of normal supersolvable subgroups. Proc. Am. Math. Soc. 30(1), 46–48 (1971)

  7. 7.

    Vasilyev, A.F., Vasilyeva, T.I.: On finite groups whose chief factors are simple groups. Russian Math. (Iz. VUZ) 41(11), 8–12 (1997)

  8. 8.

    Su, X.: On semi-normal subgroups of finite group. J. Math. (Wuhan) 8(1), 7–9 (1988)

  9. 9.

    Monakhov, V.S., Trofimuk, A.A.: Finite groups with two supersoluble subgroups. J. Group Theory. 22, 297–312 (2019)

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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).

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

Mathematics Subject Classification

  • 20D10
  • 20D20