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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2016 Volume 443, Pages 106–132 (Mi znsl6261)

This article is cited in 2 papers

Reduction theorems for triples of short root subgroups in Chevalley groups

V. V. Nesterov

Baltic State Technical University, St. Petersburg, Russia

Abstract: In the present paper we prove the reduction theorems for triple short root unipotent subgroups in Chevalley groups of type $\mathrm B_\ell$ and $\mathrm C_\ell$. The main result roughly speaking is the following. Any subgroup generated by a triple of subgroups in question (apart from one case) is conjugate to a subgroup of
$$ G(\mathrm B_4,K)U(\mathrm B_5,K)\quad\mathrm{or}\quad G(\mathrm C_4,K)U(\mathrm C_5,K), $$
respectively.

Key words and phrases: Chevalley groups, root subgroups, unipotent radical.

UDC: 512.542.6

Received: 02.06.2015


 English version:
Journal of Mathematical Sciences (New York), 2017, 222:4, 437–452

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© Steklov Math. Inst. of RAS, 2025