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On finite J-groups

  • A. Ballester-Bolinches (a1) and R. Esteban-Romero (a2)

Abstract

Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.

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References

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[2]Bianchi, M., Mauri, A. Gillio Berta, Herzog, M. and Verardi, L., ‘On finite solvable groups in which normality is a transitive relations’, J. Group Theory 3 (2000), 147156.
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[9]Peng, T. A., ‘Finite groups with pronormal subgroups’, Proc. Amer Math. Soc. 20 (1969), 232234.
[10]Robinson, D. J. S., ‘A note on finite groups in which normality is transitive’, Proc. Amer Math. Soc. 19 (1968), 933937.
[11]Robinson, D. J. S., A course in the theory of groups (Springer, New York, 1982).
[12]Rose, J., The abnormal structure of finite groups (Ph.D. Thesis, Cambridge, 1964).
[13]Sementovskiı, V.G., ‘Pronormal subgroups of finite groups’, Vescī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 135 (1973), 1216.
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