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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 479–507 (Mi izv1498)  

This article is cited in 8 scientific papers (total in 8 papers)

On a problem of Szép

L. S. Kazarin


Abstract: It is proved that, if $G$ is a finite group representable as a product of an Abelian group $A$ and a group $B$, then the center of $B$ is contained in a solvable normal subgroup of $G$. The disposition of $O_p(Z(B))$ in the upper $p$-series of a finite solvable group $G$ having a factorization of this sort is determined. A corollary for locally finite groups is provided.
Bibliography: 33 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 467–495

Bibliographic databases:

UDC: 512.54
MSC: Primary 20D40; Secondary 20D10, 20E25
Received: 24.05.1982
Revised: 14.10.1985

Citation: L. S. Kazarin, “On a problem of Szép”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 479–507; Math. USSR-Izv., 28:3 (1987), 467–495

Citation in format AMSBIB
\Bibitem{Kaz86}
\by L.~S.~Kazarin
\paper On a~problem of Sz\'ep
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 479--507
\mathnet{http://mi.mathnet.ru/izv1498}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854593}
\zmath{https://zbmath.org/?q=an:0614.20014|0602.20028}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 467--495
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000894}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. S. Kazarin, L. A. Kurdachenko, “Finiteness conditions and factorizations in infinite groups”, Russian Math. Surveys, 47:3 (1992), 81–126  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. N. Tyutyanov, “Products of $\pi$-nilpotent subgroups”, Sb. Math., 187:9 (1996), 1349–1354  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Silvana Franciosi, Francesco de Giovanni, Yaroslav P. Sysak, “An extension of the Kegel–Wielandt theorem to locally finite groups”, Glasgow Math J, 38:2 (1996), 171  crossref
    4. Bernhard Amberg, Lev S. Kazarin, “On finite products of soluble groups”, Isr J Math, 106:1 (1998), 93  crossref  mathscinet  zmath  isi  elib
    5. Bernhard Amberg, Lev Kazarin, “On the product of a nilpotent group and a group with non-trivial center”, Journal of Algebra, 311:1 (2007), 69  crossref
    6. L.S. Kazarin, A. Martínez-Pastor, M.D. Pérez-Ramos, “On the product of a π-group and a π-decomposable group”, Journal of Algebra, 315:2 (2007), 640  crossref
    7. L. S. Kazarin, “Konechnye gruppy s faktorizatsiei”, Tr. In-ta matem., 16:1 (2008), 40–46  mathnet
    8. L.S. Kazarin, A. Martínez-Pastor, M.D. Pérez-Ramos, “A reduction theorem for a conjecture on products of two π-decomposable groups”, Journal of Algebra, 379 (2013), 301  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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