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Keywords:
abnormal subgroups; $U$-subgroups; counternormal subgroups
abnormal subgroups; $U$-subgroups; counternormal subgroups
Summary:
The article is dedicated to groups in which the set of abnormal and normal subgroups ($U$-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
References:
[BB] Ba M.S., Borevich Z.I.: On arrangement of intermediate subgroups. in: Rings and Linear Groups, Kubansk. Univ., Krasnodar, 1988, pp.14-41. MR 1206023
[C] Carter R.W.: Nilpotent self-normalizing subgroups of soluble groups. Math. Z. 75 (1961), 136-139. MR 0123603 | Zbl 0168.27301
[DeFKS] De Falco M., Kurdachenko L.A., Subbotin I.Ya.: Groups with only abnormal and subnormal subgroups. Atti Sem. Mat. Fis. Univ. Modena 46 2 (1998), 435-442. MR 1665935 | Zbl 0918.20017
[F] Fatahi A.: Groups with only normal and abnormal subgroups. J. Algebra 28 (1974), 15-19. MR 0335628
[KS] Kurdachenko L.A., Subbotin I.Ya.: On transitivity of abnormality. Publ. Math. Debrecen 61 (2002), 3-4 479-486. MR 1943708 | Zbl 1012.20030
[KS1] Kurdachenko L.A., Subbotin I.Ya.: On U-normal subgroups. Southeast Asian Bull. Math. 26 (2003), 789-801. MR 2045113 | Zbl 1055.20027
[KS2] Kurdachenko L.A., Subbotin I.Ya.: Abnormal subgroups and Carter subgroups in some infinite groups. Algebra Discrete Math. 1 (2005), 69-83. MR 2148821 | Zbl 1092.20027
[KNS] Kuzennyi N.F., Subbotin I.Ya: New characterization of locally nilpotent $øverline{IH}$-groups. Ukrain. Mat. Zh. 40 (1988), 322-326 English translation: Ukrainian Math. J. 40 (1988), 274-277. MR 0952119
[K] Kurosh A.G.: The Theory of Groups. American Mathematical Society, Providence, 1979. Zbl 0111.02502
[LR] Lennox J.C., Robinson D.J.S.: The Theory of Infinite Soluble Groups. Oxford Mathematical Monographs, Oxford University Press, Oxford, 2004. MR 2093872 | Zbl 1059.20001
[R] Rose J.S.: Nilpotent subgroups of finite soluble groups. Math. Z. 106 (1968), 97-112. MR 0252516 | Zbl 0169.03402
[RD] Robinson D.J.S.: A Course in the Theory of Groups. Springer, New York, 1982. MR 0648604 | Zbl 0836.20001
[S] Subbotin I.Ya.: Groups with alternatively normal subgroups. Izv. Vyssh. Uchebn. Zaved. Mat. 3 (1992), 86-88 English translation: Soviet. Math. 3 (1992), 87-89. MR 1204823 | Zbl 0816.20030
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