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Infinite Groups Containing a Proper Hughes Subgroup H3(G)

Algebra and Logic Aims and scope

We consider groups in which H3(G) is both nontrivial and proper. In particular, it is proved that in such a group, |G : H3(G)| = 3.

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References

  1. D. R. Hughes and J. G. Thompson, “The Hp-problem and the structure of Hp-groups,” Pac. J. Math., 9, 1097-1101 (1959).

    Article  Google Scholar 

  2. O. H. Kegel, “Die Nilpotenz der Hp-Gruppen,” Math. Z., 75, 373-376 (1961).

    Article  Google Scholar 

  3. E. I. Khukhro, “On locally nilpotent groups admitting a splitting automorphism of prime order,” Mat. Sb., 130, No. 1, 120-127 (1986).

    MATH  Google Scholar 

  4. E. I. Khukhro, “Construction of finite p-groups that admit partitions,” Sib. Math. J., 30, No. 6, 1010-1019 (1989).

    Article  Google Scholar 

  5. E. I. Khukhro, “Nilpotency of solvable groups admitting a splitting automorphism of prime order,” Algebra and Logic, 19, No. 1, 77-84 (1980).

  6. A. Kh. Zhurtov, D. V. Lytkina, and V. D. Mazurov, “Primary cosets in groups,” Algebra and Logic, 59, No. 3, 216-221 (2020),

  7. Yu. P. Razmyslov, “On Lie algebras satisfying the Engel condition,” Algebra and Logic, 10, No. 1, 21-29 (1971).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    W. Guo

  2. School of Science, Hainan University, Haikou, Hainan, P.R. China

    W. Guo

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    D. V. Lytkina & V. D. Mazurov

  4. Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia

    D. V. Lytkina

Authors
  1. W. Guo
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  2. D. V. Lytkina
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  3. V. D. Mazurov
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Corresponding author

Correspondence to W. Guo.

Additional information

Supported by the NNSF of China (grant No. 12171126) and by Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province.

Supported byMathematical Center in Akademgorodok, Agreement with RFMinistry of Education and Science No. 075-15-2019-1613.

Supported by RFBR (project No. 20-51-00007) and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0001).

Translated from Algebra i Logika, Vol. 60, No. 3, pp. 298-302, May-June, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.303.

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Guo, W., Lytkina, D.V. & Mazurov, V.D. Infinite Groups Containing a Proper Hughes Subgroup H3(G). Algebra Logic 60, 196–199 (2021). https://doi.org/10.1007/s10469-021-09641-z

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  • DOI: https://doi.org/10.1007/s10469-021-09641-z

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