Abstract
We study groups whose structure is similar to the structure of metacyclic groups. These groups play an important role in the investigation of groups with normal subgroups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Huppert, Endliche Gruppen I, Springer, Berlin etc. (1967).
N. Blackburn, “Generalization of certain elementary theorems on p-groups,” Proc. London Math. Soc, 11, No. 41, 1–22 (1961).
N. Blackburn, “On a special class of p-groups,” Proc. Cambridge Phil. Soc, 53, 19–57 (1957).
A. D. Ustyuzhaninov, “Finite 2-groups with three involutions,” Sib. Mat. Zh., 13, No. 1, 182–197 (1972).
J. Karsten, “Uber 2 -Gruppen, in denen jede abelsche Untergruppe von hochstens 2 Elementen erzeugt wirt,” J. Algebra, 30, 31–36 (1974).
M. Curcio, “Classification on finite minimal nonmetacyclic groups,” Acta Soc. Math., 47, No. 3–4, 289–295 (1984).
N. N. Semko and N. F. Kuzennyi, Structure of Metacyclic Meta-Hamiltonian Groups [in Russian], Kiev Pedagogical Institute, Kiev (1983).
N. F. Kuzennyi and N. N. Semko, “Structure of solvable meta-Hamiltonian groups”, Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 6–8 (1985).
N. N. Semko and N. F. Kuzennyi, “Structure of metacyclic meta-Hamiltonian groups,” in: Contemporary Analysis and Its Applications [in Russian], Naukova Dumka, Kiev (1989), pp. 173–183.
M. Hall (Jr.), The Theory of Groups, Macmillan Company, New York 1959.
S. S. Levishchenko, N. F. Kuzennyi, and N. N. Semko, Constructive Description of Finite Minimal Nonmetacyclic Groups [in Russian], Deposited at UkrNIINTI, No. 33-Uk 87, Kiev (1986).
N. N. Semko, “Structure of locally metacyclic groups,” in: Structure of Groups and Properties of Their Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986), pp. 83–93.
S. S. Levishchenko and N. N. Semko, “Constructive description of finite nonsupersolvable groups all 2-maximal subgroups of which are metacyclic,” in: Investigations of Groups with Restrictions Imposed on Their Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 42–51.
N. N. Semko, S. S. Levishchenko, and N. F. Kuzennyi, “Finite nonsupersolvable groups all 2-maximal subgroup of which are metacyclic,” in: Abstracts of the Xth All-Union Symposium on the Theory of Groups [in Russian], Institute of Mathematics, Belorussian Academy of Sciences, Minsk (1986), p. 208.
S. S. Levishchenko, N. F. Kuzennyi, N. N. Semko, and L. Tomanek, “Structure of finite minimal nonmetacyclic groups,” in: Prirod-ne vedy. Matematika. Zbornik Pedagogickej Fakulty v Presove Univerzity P. I. Safarika, Proc. XXIV, Zvazok I, Kosice (1990), pp. 49–97.
A. G. Kurosh, Theory of Groups [in Russian], Nauka, Moscow 1967.
S. N. Chernikov, Groups with Prescribed Properties of Systems of Subgroups [in Russian], Nauka, Moscow 1980.
N. Herstein, “A remark on finite groups,” Proc. Amer. Math. Soc., 9, No. 2, 255–257 (1958).
Rights and permissions
About this article
Cite this article
Kuzennyi, N.F., Semko, N.N. On groups close to metacyclic groups. Ukr Math J 48, 880–889 (1996). https://doi.org/10.1007/BF02384173
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384173