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On Certain Properties of Subnormal Subgroups

  • Jennifer Whitehead (a1)

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Main results. Let G be a group generated by two subnormal subgroups H and K. Denoting the class of nilpotent groups by 𝔑, and the limit of the lower central series by G𝔑, Wielandt showed in [14], for groups with a composition series that

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References

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1. Baer, R., Irreducible groups of automorphisms of abelian groups, Pacific J. Math. 1 (1964), 385406.
2. Brewster, D., A criterion for the permutability of subnormal subgroups, J. Algebra 36 (1975), 8587.
3. Drukker, M., Robinson, D. J. S. and Stewart, I. N., The subnormal coalescence of some classes of groups of finite rank, J. Austral. Math. Soc. 16 (1973), 324327.
4. Hartley, B. and Peng, T. A., Subnormality, ascendancy and the minimal condition, J. Algebra 41 (1976), 5878.
5. Kegel, O. H., Uber den Normalisator von subnormalen und erreichbaren Untergruppen, Math. Ann. 163 (1966), 248258.
6. McLain, D. H., On locally nilpotent groups, Proc. Cambridge Philos. Soc. 52 (1956), 511.
7. Mal'cev, A. I., Homomorphisms of finite groups, Ivanov. gosudarst. ped. Inst, ucenyc. Zapiski. fiz-mat. Nauki. 18 (1958), 4960.
8. Peng, T. A., A criterion for subnormality, Arch, der Math. 26 (1975), 225230.
9. Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Part 1 (Springer Berlin/Heidelberg/New York, 1972).
10. Roseblade, J. E., A note on subnormal coalition classes, Math. Z. DO (1965), 373375.
11. Roseblade, J. E., The derived series of the join of subnormal subgroups, Math. Z. 117 (1970), 5769.
12. Roseblade, J. E. and Stonehewer, S. E., Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423435.
13. Stonehewer, S. E., Nilpotent residuals of subnormal subgroups, Math. Z. 130, (1974), 4554.
14. Wielandt, H., Vertauschbare nachinvariante Untergruppen, Abh. Math. Sem. Univ. Hamburg 21 (1957), 5562.
15. Wielandt, H., Kriterien fiir Subnormalitàt in endlichen Gruppen, Math. Z. 138 (1974), 199203.
16. Zassenhaus, H., The theory of groups, 2nd ed. (Chelsea, New York, 1958).
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On Certain Properties of Subnormal Subgroups

  • Jennifer Whitehead (a1)

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