Ukrainian Mathematical Journal

, Volume 50, Issue 5, pp 842–845 | Cite as

On subgroups lifting modulo central commutant

  • V. V. Sergeichuk
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Abstract

We consider a finitely generated group G with the commutant of odd order \(p_1^{n_1 } \ldots p_s^{n_s } \) located at the center and prove that there exists a decomposition of G/G′ into the direct product of indecomposable cyclic groups such that each factor except at most n l + ... + n s factors lifts modulo commutant.

Keywords

Direct Product Cyclic Group Prime Order Direct Factor Ukrainian Academy 

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References

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    B. Huppert, Endlishe Gruppen, Springer, Berlin (1967).Google Scholar
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    V. V. Sergeichuk, “On classification of metabelian groups,” in: Matrix Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1977), pp. 151–161.Google Scholar
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    V. V. Sergeichuk, “Finitely generated groups with commutant of prime order,” Ukr. Mat. Zh., 30, No. 6, 789–795 (1978).MathSciNetGoogle Scholar
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    O. O. Mazurok, “Groups with elementary Abelian commutant of at most p 2 th order,” Ukr. Mat. Zh., 50, No. 4, 534–539 (1998).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. V. Sergeichuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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