Abstract
We describe locally solvable groups G such that all their infinite subgroups that do not belong to a certain proper subgroup of the group under consideration are normal.
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REFERENCES
M. F. Kuzennyi and M. M. Semko, “Structure of separable Dedekind groups,” Ukr. Mat. Zh., 48, No. 10, 1342–1351 (1996).
O. O. Odintsova, “On the derived length of H(ICS)-groups,” Collected Scientific Works of the Dragomanov Pedagogic University [in Ukrainian], National Pedagogic University, Kiev (1999), pp. 201–204.
O. O. Odintsova, “Groups with systems of separable normal subgroups,” in: Fractal Analysis and Related Problems [in Ukrainian], Issue 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 211–214.
D. I. Zaitsev, “On solvable subgroups of locally solvable groups,” Dokl. Akad. Nauk. SSSR, 21, No. 6, 1250–1253 (1974).
M. F. Kuzennyi and M. M. Semko, Meta-Hamiltonian Groups and Their Generalizations [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996).
S. N. Chernikov, Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).
D. Cappit, “Generalized Dedekind groups,” J. Algebra, 17, No. 3, 310–316 (1971).
D. I. Zaitsev, “On complementability of subgroups in extremal groups,” in: Investigation of Groups with Given Properties of Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1974), pp. 72–130.
M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1982).
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Odintsova, O.O. On One Class of Separable Dedekind Groups. Ukrainian Mathematical Journal 53, 306–311 (2001). https://doi.org/10.1023/A:1010481407371
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DOI: https://doi.org/10.1023/A:1010481407371