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Algebra Logika, 2012, Volume 51, Number 3, Pages 331–346 (Mi al538)  

This article is cited in 9 scientific papers (total in 9 papers)

Twisted conjugacy classes in general and special linear groups

T. R. Nasybullov

Novosibirsk State University, Novosibirsk, Russia

Abstract: We consider twisted conjugacy classes and the $R_\infty$-property for classical linear groups. In particular, it is stated that the general linear group $\mathrm{GL}_n(K)$ and the special linear group $\mathrm{SL}_n(K)$, for $n\ge3$, possess the $R_\infty$-property if either $K$ is an infinite integral domain with trivial automorphism group, or $K$ is an integral domain containing a subring of integers, whose automorphism group $\operatorname{Aut}(K)$ is finite. By an integral domain we mean a commutative ring with identity which has no zero divisors.

Keywords: linear group, twisted conjugacy classes, automorphism group, integral domain.

Full text: PDF file (176 kB)
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English version:
Algebra and Logic, 2012, 51:3, 220–231

Bibliographic databases:

UDC: 512.54
Received: 10.03.2012
Revised: 03.04.2012

Citation: T. R. Nasybullov, “Twisted conjugacy classes in general and special linear groups”, Algebra Logika, 51:3 (2012), 331–346; Algebra and Logic, 51:3 (2012), 220–231

Citation in format AMSBIB
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\by T.~R.~Nasybullov
\paper Twisted conjugacy classes in general and special linear groups
\jour Algebra Logika
\yr 2012
\vol 51
\issue 3
\pages 331--346
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013908}
\zmath{https://zbmath.org/?q=an:1264.20046}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 3
\pages 220--231
\crossref{https://doi.org/10.1007/s10469-012-9185-6}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866152129}


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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. Mubeena T., Sankaran P., “Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups”, Transform. Groups, 19:1 (2014), 159–169  crossref  mathscinet  zmath  isi  elib  scopus
    2. T. R. Nasybullov, “Twisted conjugacy classes in Chevalley groups”, Algebra and Logic, 53:6 (2015), 481–501  mathnet  crossref  mathscinet  isi
    3. Fel'shtyn A., Goncalves D., Wong P., “Twisted Conjugacy Classes For Polyfree Groups”, Commun. Algebr., 42:1 (2014), 130–138  crossref  mathscinet  zmath  isi  scopus
    4. Dekimpe K., Goncalves D., “the R Infinity Property For Abelian Groups”, Topol. Methods Nonlinear Anal., 46:2 (2015), 773–784  mathscinet  zmath  isi
    5. Fel'shtyn A., Troitsky E., “Aspects of the Property R-Infinity”, J. Group Theory, 18:6 (2015), 1021–1034  crossref  mathscinet  zmath  isi  scopus
    6. T. R. Nasybullov, “The $R_{\infty}$-property for chevalley groups of types $B_l$, $C_l$, $D_l$ over integral domains”, J. Algebra, 446 (2016), 489–498  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. Fel'shtyn, T. Nasybullov, “The $R_{\infty}$ and $S_{\infty}$ properties for linear algebraic groups”, J. Group Theory, 19:5 (2016), 901–921  crossref  mathscinet  zmath  isi  scopus
    8. E. V. Troitskii, “Dva primera, svyazannye so skruchennoi teoriei Bernsaida–Frobeniusa dlya beskonechno porozhdënnykh grupp”, Fundament. i prikl. matem., 21:5 (2016), 219–227  mathnet
    9. A. L. Fel'shtyn, E. V. Troitsky, “Twisted Burnside–Frobenius theory for endomorphisms of polycyclic groups”, Russ. J. Math. Phys., 25:1 (2018), 17–26  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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