Abstract
We prove that the condition of periodicity of all normal Abelian subgroups of a group with increasing normal series with cyclic factors such that infinite factors are central is preserved on passing to subgroups of finite index. We present an example which demonstrates that the requirement that all infinite cyclic factors must be central cannot be omitted.
References
J. S. Wilson, “Some properties of groups inherited by normal subgroups of finite index,”Math. Z.,114, No. 1, 19–21 (1970).
D. I. Zaitsev, “On the properties of groups inherited by their normal subgroups,”Ukr. Mat. Zh.,38, No. 6, 707–713 (1986).
D. I. Zaitsev, “Complementability of subgroups in extremal groups,” in:Investigation of Groups According to Given Properties of Their Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1974), pp. 72–130.
S. A. Chechin, “On one property of hypercyclic groups,” in:Abstracts of the XIX All-Union Algebraic Conference [in Russian], Vol. 2, L'vov (1987), p. 313.
S. A. Chechin, “On the minimality condition for normal divisors,” in:Abstracts of the XV All-Union Algebraic Conference [in Russian], Vol. 1 (1979), p. 175.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 436–438, March, 1995.
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Chechin, S.A. On one property of hypercyclic groups. Ukr Math J 47, 509–512 (1995). https://doi.org/10.1007/BF01056318
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DOI: https://doi.org/10.1007/BF01056318