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Mat. Sb., 2016, Volume 207, Number 6, Pages 27–52 (Mi msb8580)  

This article is cited in 6 scientific papers (total in 6 papers)

On complements of coradicals of finite groups

V. A. Vedernikova, M. M. Sorokinab

a Moscow City Pedagogical University
b I. G. Petrovsky Bryansk State University

Abstract: Let $\mathfrak F$ be an $\omega$-local Fitting formation, and $G$ a finite group that can be represented in the form of a product of $n$ subnormal subgroups whose $\mathfrak F$-coradicals are $\omega$-soluble, and whose Sylow $p$-subgroups are abelian for any $p\in\omega$. It is established that there exist $\omega$-complements of the $\mathfrak F$-coradical of $G$. New theorems on the existence of complements of coradicals of a group are obtained as corollaries. For an $\omega$-local formation $\mathfrak F$, conditions are established for the existence of complements and $\omega$-complements of the $\mathfrak F$-coradical of a group in any of its extensions.
Bibliography: 21 titles.

Keywords: finite group, Fitting class, $\omega$-local formation, coradical of a group, $\omega$-complement of a subgroup.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8580

Full text: PDF file (603 kB)
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English version:
Sbornik: Mathematics, 2016, 207:6, 792–815

Bibliographic databases:

UDC: 512.542
MSC: Primary 20F17; Secondary 20D10, 20D20, 20D35
Received: 30.07.2015 and 28.11.2015

Citation: V. A. Vedernikov, M. M. Sorokina, “On complements of coradicals of finite groups”, Mat. Sb., 207:6 (2016), 27–52; Sb. Math., 207:6 (2016), 792–815

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. F. Kamornikov, O. L. Shemetkova, “O dopolnenii koradikala konechnoi gruppy”, PFMT, 2017, no. 4(33), 58–64  mathnet
    2. V. A. Vedernikov, M. M. Sorokina, “The $\mathfrak F^\omega$-normalizers of finite groups”, Siberian Math. J., 58:1 (2017), 49–62  mathnet  crossref  crossref  isi  elib  elib
    3. X. Yi, S. F. Kamornikov, “On Shemetkov's theorem about the complementedness of the residual”, Siberian Math. J., 59:2 (2018), 276–282  mathnet  crossref  crossref  isi  elib
    4. S. F. Kamornikov, O. L. Shemetkova, “O dopolneniyakh koradikala v rasshireniyakh konechnykh grupp”, PFMT, 2018, no. 3(36), 80–83  mathnet
    5. Kamornikov S.F. Shemetkova O.L., “On the Existence of Complements of Residuals of Finite Group”, J. Algebra, 533 (2019), 344–352  crossref  mathscinet  zmath  isi
    6. M. M. Sorokina, S. P. Maksakov, “On the Normality of $\mathfrak F^{\omega}$-Abnormal Maximal Subgroups of Finite Groups”, Math. Notes, 108:3 (2020), 409–418  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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