This article is cited in 6 papers

Solvable and unipotent supergroups

A. N. Zubkov^a, P. A. Ulyashev<sup>b

a</sup> 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.

UDC: 512.55

Received: 26.04.2013
Revised: 04.03.2014

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

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