Abstract
We obtain a characterization of not finitely generated groups with maximality condition for nonhypercentral (respectively, nonnilpotent) subgroups.
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REFERENCES
L. Rédei, “Die endlichen einstufig nichtnilpotenten Gruppen,” Publ. Math. (Debrecen), 4, 303–324 (1965).
M. F. Newman and L. Wiegold, “Groups with many nilpotent subgroups,” Arch. Math., 15, 241–250 (1964).
H. Heineken and I. J. Mohamed, “A group with trivial centre satisfying the normalizer condition,” J. Algebra, 10, 368–376 (1968).
J. D. Meldrum, “On the Heineken – Mohamed groups,” J. Algebra, 27, 437–444 (1973).
B. Hartley, “A note on the normalizer condition,” Proc. Cambridge Phil. Soc., 74, 11–15 (1973).
B. Bruno and R. E. Philips, “On multipliers of Heineken–Mohamed type groups,” Rend. Semin. Mat. Univ. Padova, 85, 133–146 (1991).
F. Menagazzo, “Groups of Heineken–Mohamed,” J. Algebra, 171, 807–825 (1995).
W. Möhres, “Auflösbarkeit von Gruppen deren Untergruppen alle subnormal sind,” Arch. Math., 54, 232–235 (1990).
O. D. Artemovych, “On indecomposable groups and groups with hypercentral-by-finite proper subgroups,” Publ. Math. (Debrecen), 53, 163–175 (1998).
S. N. Chernikov, Groups with Given Properties of Systems of Subgroups [in Russian], Nauka, Moscow (1980).
V. P. Shunkov, “On abstract characterizations of certain linear groups,” in: Algebra. Matrices and Matrix Groups [in Russian], Krasnoyarsk (1970), pp. 3–54.
D. I. Zaitsev and L. A. Kudryachenko, “Groups with maximality condition for non-Abelian groups,” Ukr. Mat. Zh., 43, No. 7–8, 926–930 (1991).
O. D. Artemovich, “Groups with maximality condition for nonhypercentral subgroups,” Visn. Kyiv. Univ., Ser. Fiz.-Mat., Issue 4, 9–11 (1999).
O. D. Artemovych, “On solvable periodic groups with maximality condition for subgroups that are not almost hypercentral,” Visn. Kyiv. Univ., Ser. Fiz.-Mat., Issue 1, 27–30 (2000).
O. D. Artemovych, “Locally solvable groups with maximal condition for nonhypercentral subgroups,” Dopov. Nats. Akad. Nauk Ukr., Ser. Fiz.-Mat., No. 9, 42–44 (2001).
M. R. Dixon and L. A. Kurdachenko, “Groups with the maximum condition on non-nilpotent subgroups,” J. Group Theory, 4, 75–87 (2001).
M. R. Dixon and L. A. Kurdachenko, “Locally nilpotent groups with the maximum condition on non-nilpotent subgroups,” Glasgow Math. J., 43, 85–102 (2001).
D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972).
L. Fuchs, Infinite Abelian Groups, Vol. 2, Academic Press, New York–London (1973).
D. W. Sharpe and P. Vamos, Injective Modules, Cambridge University Press, Cambridge (1972).
Xu Maoqian, “Groups whose proper subgroups are Baer groups,” Acta Math. Sinica (New Ser.), 12, 10–17 (1996).
G. Baumslag, “Wreath product and p-groups,” Proc. Cambridge Phil. Soc., 55, 224–231 (1959).
W. Móhres, “Torsiongruppen, deren Untergruppen alle subnormal sind,” Geom. Dedic., 31, 237–248 (1989).
B. Bruno and R. E. Philips, “A note on groups with nilpotent-by-finite proper subgroups,” Arch. Math., 65, 369–374 (1995).
A. O. Asar, “On non-nilpotent p-groups and the normalizer condition,” Turk. J. Math., 18, 114–129 (1994).
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Artemovich, O.D. Groups with Maximality Condition for Nonhypercentral Subgroups. Ukrainian Mathematical Journal 54, 1075–1085 (2002). https://doi.org/10.1023/A:1022094907343
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DOI: https://doi.org/10.1023/A:1022094907343