This article is cited in 2 papers

Affine algebraic groups with periodic components

S. N. Fedotov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finitely many fixed points. Also discussed is which connected groups have finite extensions with periodic components. The results are applied to the study of the normalizer of a maximal torus in a simple algebraic group.
Bibliography: 10 titles.

Keywords: linear algebraic group, algebraic torus, finite-order element, regular automorphism, Coxeter element.

UDC: 512.743

MSC: Primary 14L17; Secondary 17B40, 17B45, 20G20

Received: 23.05.2008 and 13.04.2009

DOI: 10.4213/sm6368

 English version: Sbornik: Mathematics, 2009, 200:7, 1089–1104

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