Abstract
We introduce the notion of CDN[)-groups:G is a CDN[)-group if, for any pair of its subgroupsA andB such thatA is a proper nonmaximum subgroup, ofB, there exists a normal subgroupN which belongs toG and satisfies the inequalitiesA≤N<B. Fifteen types of nilpotent non-Dedekind groups and nine types of nonnilpotent locally graded groups of this kind are obtained.
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References
M. M. Semko, “On the structure of locally graded CDN(]-groups”Ukr. Mat., Zh.,50, No. 11, 1532–1536 (1998).
M. M. Semko,Groups with Conditions for the Density of Normality and Its Generalizations for Some Systems of Subgroups [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
S. S. Levishchenko and N. F. Kuzennyi,Finite Groups with Systems of Dispersive Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1997).
M. F. Kuzennyi and M. M. Semko,Meta-Hamiltonian Groups and Their Generalization [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996).
Additional information
Ukrainian Economic Financial Institute, Irpen. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 383–388, March, 1999.
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Semko, M.M. Structure of locally graded CDN[)-groups. Ukr Math J 51, 427–433 (1999). https://doi.org/10.1007/BF02592479
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DOI: https://doi.org/10.1007/BF02592479