Abstract
We determine the structure of finite minimal nondispersible groups each nonmetacyclic subgroup of which is normal (Theorem 2) and describe all finite nondispersible groups each nonmetacyclic subgroup of which is normal (Theorem 3).
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References
R. Dedekind, “Uber Gruppen, deren sammtliche Teiler Normalteiler sind,”Math. Ann.,48, 548–561 (1897).
E. Best and O. Taussky, “A class of groups,”Proc. PJA. Sect. A,47, 55–62 (1942).
G. M. Romalis, “On meta-Hamiltonian groups,”Usp. Mat. Nauk,17, No. 6, 228 (1962).
S. N. Chernikov, “Infinite groups with given properties of systems of their infinite subgroups,”Dokl. Akad. Nauk SSSR,159, 759–760 (1964).
D. Cappit, “Generalized Dedekind groups,”J. Algebra,17, No. 3, 310–316 (1971).
S. S. Levishchenko, N. F. Kuzennyi, and M. M. Semko,Constructive Description of Finite Minimal Nonmetacyclic Groups [in Russian], Dep. UkrNIINTI No. 33, Kiev (1987).
S. S. Levishchenko and N. F. Kuzennyi,Groups with Dispersibility Conditions for Subgroups. Manual [in Russian], Kiev Pedagogical Institute, Kiev 1985.
B. Huppert,Endliche Gruppen, Springer, Berlin 1967.
M. Hall,The Theory of Groups, Macmillan, New York 1959.
D. I. Zaitsev, “On the 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.
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Kovalenko, V.I. Structure of finite nondispersible groups each nonmetacyclic subgroup of which is normal. Ukr Math J 48, 1517–1521 (1996). https://doi.org/10.1007/BF02377820
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DOI: https://doi.org/10.1007/BF02377820