On Certain Properties of Subnormal Subgroups
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 573-582

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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(*)
Whitehead, Jennifer. On Certain Properties of Subnormal Subgroups. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 573-582. doi: 10.4153/CJM-1978-050-5
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[1] 1. Baer, R., Irreducible groups of automorphisms of abelian groups, Pacific J. Math. 1 (1964), 385–406. Google Scholar

[2] 2. Brewster, D., A criterion for the permutability of subnormal subgroups, J. Algebra 36 (1975), 85–87. Google Scholar

[3] 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), 324–327. Google Scholar

[4] 4. Hartley, B. and Peng, T. A., Subnormality, ascendancy and the minimal condition, J. Algebra 41 (1976), 58–78. Google Scholar

[5] 5. Kegel, O. H., Uber den Normalisator von subnormalen und erreichbaren Untergruppen, Math. Ann. 163 (1966), 248–258. Google Scholar

[6] 6. McLain, D. H., On locally nilpotent groups, Proc. Cambridge Philos. Soc. 52 (1956), 5–11. Google Scholar

[7] 7. Mal'cev, A. I., Homomorphisms of finite groups, Ivanov. gosudarst. ped. Inst, ucenyc. Zapiski. fiz-mat. Nauki. 18 (1958), 49–60. Google Scholar

[8] 8. Peng, T. A., A criterion for subnormality, Arch, der Math. 26 (1975), 225–230. Google Scholar

[9] 9. Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Part 1 (Springer Berlin/Heidelberg/New York, 1972). Google Scholar

[10] 10. Roseblade, J. E., A note on subnormal coalition classes, Math. Z. DO (1965), 373–375. Google Scholar

[11] 11. Roseblade, J. E., The derived series of the join of subnormal subgroups, Math. Z. 117 (1970), 57–69. Google Scholar

[12] 12. Roseblade, J. E. and Stonehewer, S. E., Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423–435. Google Scholar

[13] 13. Stonehewer, S. E., Nilpotent residuals of subnormal subgroups, Math. Z. 130, (1974), 45–54. Google Scholar

[14] 14. Wielandt, H., Vertauschbare nachinvariante Untergruppen, Abh. Math. Sem. Univ. Hamburg 21 (1957), 55–62. Google Scholar

[15] 15. Wielandt, H., Kriterien fiir Subnormalitàt in endlichen Gruppen, Math. Z. 138 (1974), 199–203. Google Scholar

[16] 16. Zassenhaus, H., The theory of groups, 2nd ed. (Chelsea, New York, 1958). Google Scholar

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