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Uspekhi Mat. Nauk, 1977, Volume 32, Issue 5(197), Pages 3–68 (Mi umn3237)  

This article is cited in 4 scientific papers (total in 4 papers)

Varieties of group representations

B. I. Plotkin


Abstract: A group representation is a pair $(A,\Gamma)$, where $A$ is a module over a commutative ring $K$ with identity and $\Gamma$ is a group that acts on $A$. In the category of group representations over a fixed $K$, both $A$ and $\Gamma$ are variable. We study varieties in this category. This paper is a survey of results and problems in this area and connections with other topics.

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English version:
Russian Mathematical Surveys, 1977, 32:5, 1–72

Bibliographic databases:

UDC: 519.4
MSC: 20M07, 20E10, 20M30, 20M50
Received: 15.05.1976

Citation: B. I. Plotkin, “Varieties of group representations”, Uspekhi Mat. Nauk, 32:5(197) (1977), 3–68; Russian Math. Surveys, 32:5 (1977), 1–72

Citation in format AMSBIB
\Bibitem{Plo77}
\by B.~I.~Plotkin
\paper Varieties of group representations
\jour Uspekhi Mat. Nauk
\yr 1977
\vol 32
\issue 5(197)
\pages 3--68
\mathnet{http://mi.mathnet.ru/umn3237}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=470082}
\zmath{https://zbmath.org/?q=an:0373.20038|0386.20005}
\transl
\jour Russian Math. Surveys
\yr 1977
\vol 32
\issue 5
\pages 1--72
\crossref{https://doi.org/10.1070/RM1977v032n05ABEH003867}


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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. B. I. Plotkin, “Varieties in representations of finite groups. Locally stable varieties. Matrix groups and varieties of representations”, Russian Math. Surveys, 34:4 (1979), 69–103  mathnet  crossref  mathscinet  zmath
    2. A. E. Bereznyi, “Discrete groups with subexponential growth of coefficients in the Golod–Shafarevich series”, Russian Math. Surveys, 35:5 (1980), 251–252  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. N. Krasilnikov, “The identities of a group with nilpotent commutator subgroup are finitely based”, Math. USSR-Izv., 37:3 (1991), 539–553  mathnet  crossref  mathscinet  zmath  adsnasa
    4. B. I. Plotkin, “Problems in algebra inspired by universal algebraic geometry”, J. Math. Sci., 139:4 (2006), 6780–6791  mathnet  crossref  mathscinet  zmath  elib  elib
  • Успехи математических наук Russian Mathematical Surveys
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