Elements in reductive algebraic groups with Abelian connected centralizers. (Q1758255)

The author proves that, with essentially one exception, an element in a reductive algebraic group has Abelian connected centralizer if and only if it is regular. This extends a result of Kurtzke, who proved the statement (without exception) in the case of good characteristic; this assumption allowed results about the group to be deduced from calculations in its Lie algebra. By contrast, the work here relies on explicit calculations in the algebraic groups themselves.