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Algebra Logika, 2014, Volume 53, Number 3, Pages 323–339 (Mi al638)  

This article is cited in 3 scientific papers (total in 3 papers)

Solvable and unipotent supergroups

A. N. Zubkova, P. A. Ulyashevb

a Omsk State Pedagogical University, nab. Tukhachevskogo 14, Omsk, 644099, Russia
b Omsk Branch of Sobolev Institute of Mathematics, ul. Pevtsova 13, Omsk, 644099, Russia

Abstract: It is proved that an algebraic supergroup $G$ is unipotent iff $G_{ev}$ is unipotent. Here our reasoning involves only induction on dimension and some properties of the adjoint representation. In a similar way, it is shown that over a field of characteristic zero, a connected supergroup $G$ is solvable iff $G_{ev}$ is solvable.

Keywords: adjoint representation, algebraic supergroup, solvable supergroup, unipotent supergroup, connected supergroup.

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English version:
Algebra and Logic, 2014, 53:3, 206–216

Bibliographic databases:

UDC: 512.55
Received: 26.04.2013
Revised: 04.03.2014

Citation: A. N. Zubkov, P. A. Ulyashev, “Solvable and unipotent supergroups”, Algebra Logika, 53:3 (2014), 323–339; Algebra and Logic, 53:3 (2014), 206–216

Citation in format AMSBIB
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\by A.~N.~Zubkov, P.~A.~Ulyashev
\paper Solvable and unipotent supergroups
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\yr 2014
\vol 53
\issue 3
\pages 323--339
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\jour Algebra and Logic
\yr 2014
\vol 53
\issue 3
\pages 206--216
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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. A. N. Grishkov, A. N. Zubkov, “Solvable, reductive and quasireductive supergroups”, J. Algebra, 452 (2016), 448–473  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Masuoka, A. N. Zubkov, “Solvability and nilpotency for algebraic supergroups”, J. Pure Appl. Algebr., 221:2 (2017), 339–365  crossref  mathscinet  zmath  isi  scopus
    3. F. Marko, A. N. Zubkov, “Linkage principle for ortho-symplectic supergroups”, J. Algebra, 493 (2018), 444–482  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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