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. North-Holland Pub. Co. , Amsterdam 1973 . [5] L. G . Kovács . Groups with regular automorphisms of order four . Math. Z. , 75 ( 1960/61 ), 277 – 294 . [6] J. C . Lennox and D. J. S . Robinson . The Theory of Infinite Soluble Groups

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82 125 132 Doerk, K. and Hawkes, T. , Finite Soluble Groups , Walter de Gruyter, Berlin-New York, 1992

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Abstract  

A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding properties enjoyed by all the subgroups is proved. The key point is an extension of a subnormality criterion due to Wielandt.

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.1998.7964 . [3] Doerk , K. , Hawkes , T. 1992 Finite Soluble Groups De Gruyter Berlin 10.1515/9783110870138 . [4] Kegel

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Soluble Groups Walter de Gruyter Berlin – New York 10.1515/9783110870138 . [4] Fedri , V. , Serena , L. 1988 Finite soluble groups with supersoluble Sylow normalizers Arch. Math. 50 11

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] Doerk , K. and Hawkes , T. , Finite Soluble Groups , de Gruyter , Berlin/New York , 1992 . [4] Huppert , B. and Blackburn , N

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– 38 . [15] R obinson , D. J. S. , Finiteness Conditions and Generalized Soluble Groups , Springer , Berlin ( 1972 ). [16

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subgroups of Sylow p-subgroups admit a p-soluble supplement . Science China Math ., 56 : 1015 – 1018 , 2013 . [10] P . Schmidt . Subgroups permutable with all Sylow subgroups . J. Algebra , 207 : 285 – 293 , 1998 . [11] A . Shaalan . The infiuence

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References [1] W. E . Deskins . On quasinormal subgroups of finite groups . Math. Z ., 82 : 125 – 132 , 1963 . [2] K . Doerk and T.O . Hawkes . Finite Soluble Groups . de Gruyter , Berlin , 1992 . [3] Z . Han . On s -semipermutable

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solubility and supersolubility of some classes of finite groups Sci. China Ser. A 52 272 – 286 10.1007/s11425-009-0008-8 . [10] Guo

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