Skip to main content
Log in

Groups with restricted non-normal subgroups

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Baer, R.: Situation der Untergruppen und Struktur der Gruppe. S.B. Heidelberg Akad. Mat. Nat. Klasse2, 12–17 (1933)

    Google Scholar 

  2. Černikov, S.N.: On investigations of groups with properties prescribed on their subgroups. Ukrain. Mat. Z.21, 193–209 (1969)

    Google Scholar 

  3. Černikov, S.N.: Infinite non-Abelian groups with an invariance condition for infinite non-Abelian subgroups. Dokl. Akad. Nauk SSSR134, 1280–1283 (1970)

    Google Scholar 

  4. Černikov, S.N.: Infinite nonabelian groups in which all infinite non-abelian subgroups are invariant. Ukrain. Mat. Z.,23, 498–518 (1971)

    Google Scholar 

  5. Dedekind, R.: Über Gruppen, deren sämtliche Teiler Normalteiler sind. Math. Ann.48, 548–561 (1897).

    Google Scholar 

  6. Garasčuk, M.S.: Metahamiltonian linear groups. Vestnik Beloruss Gos. Univ. serI, No. 2, 89–90, 103 (1975)

    Google Scholar 

  7. Gol'fond, Yu.A.: On groups all of whose subgroups are special. Dokl. Akad. Nauk SSSR60, 1313–1315 (1948)

    Google Scholar 

  8. Gorenstein, D.: Finite groups. New York, Evanston, London: Harper and Row Publ. 1968

    Google Scholar 

  9. Gruenberg, K.W.: Residual properties of infinite soluble groups. Proc. London Math. Soc. (3)4, 29–62 (1957)

    Google Scholar 

  10. Huppert, B.: Endliche Gruppen I. Berlin, Heidelberg, New York: Springer 1967

    Google Scholar 

  11. Mahnev, A.A.: Finite metahamiltonian groups. Ural. Gos. Univ. Mat. Zap.10, No. 1, 60–75, 151 (1976)

    Google Scholar 

  12. Miller, G.A., Moreno, H.C.: Non-abelian groups in which every subgroup is abelian. Trans. Amer. Math. Soc.4, 398–404 (1903)

    Google Scholar 

  13. Nagrebeckiî, V.T.: Invariant coverings of subgroups. Ural Gos. Univ. Math. Zap.5, Tetrad 3, 91–100 (1966)

    Google Scholar 

  14. Nagrebeckiî, V.T.: Finite non-nilpotent groups, any non-abelian subgroup of which is normal. Ural Gos. Univ. Mat. Zap.6, Tetrad's 80–88 (1967)

  15. Nagrebeckiî, V.T.: Finite groups in which any non-nilpotent subgroup is invariant. Ural. Gos. Univ. Mat. Zap. J., Tetrad's 45–49 (1968)

  16. Ol'šhanskiî, A.Yu.: Infinite groups with cyclic subgroups. Dokl. Akad. Nauk SSSR,245, No. 4, 785–787 (1979)

    Google Scholar 

  17. Phillips, R.E., Wilson, J.S.: On certain minimal conditions for infinite groups. Journal of Algebra, Vol.51, No. 1, 41–68 (1978)

    Google Scholar 

  18. Robinson, D.J.S.: A theorem on finitely generated hyperabelian groups. Invent. Math.10, 38–43 (1970)

    Google Scholar 

  19. Robinson, D.J.S.: Finiteness conditions and generalized soluble groups I and II. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  20. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups. Ural Gos. Univ. Mat. Zap.5, Tetrad 3, 101–106 (1966)

    Google Scholar 

  21. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups II. Ural Gos. Univ. Mat. Zap.6, Tetrad 3, 52–58 (1968)

    Google Scholar 

  22. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups III. Ural Gos. Univ. Mat. Zap.7, Tetrad 3, 195–199 (1969–70)

    Google Scholar 

  23. Schmidt, O.J.: On groups every proper subgroup of which is special. Mat. Sb. (N.S.)31, 366–372 (1924)

    Google Scholar 

  24. Scott, W.R.: Group theory. Prentice Hall: Englewood Cliffs (1966)

    Google Scholar 

  25. Stonehewer, S.E.: Abnormal subgroups of a class of periodic locally soluble groups. Proc. London Math. Soc. (3),14, 520–536 (1964)

    Google Scholar 

  26. Wehrfritz, B.A.F.: Frattini subgroups of infinitely generated linear groups. J. London Math. Soc.43, 619–622 (1968)

    Google Scholar 

  27. Wilson, J.S.: On periodic generalized nilpotent groups. Bull. London Math. Soc.9, 81–85 (1977)

    Google Scholar 

  28. Winter, D.L.: The automorphism group of an extra-specialp-group. Rocky Mountain Journal of Math.2, No. 2, 159–168 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruno, B., Phillips, R.E. Groups with restricted non-normal subgroups. Math Z 176, 199–221 (1981). https://doi.org/10.1007/BF01261869

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01261869

Navigation