Reductive IAPS

From Apstheory

Definition

Symbol-free definition

An IAPS of groups is termed reductive with respect to a parabolic structure if every standard parabolic subgroup of it equals the corresponding Levi subgroup.

Definition with symbols

An IAPS of groups Failed to parse (Can't write to or create math temp directory): (G,\\Phi)

is termed reductivewith respect to a parabolic structure Failed to parse (Can't write to or create math temp directory): P
if for any ordered tuple of integers Failed to parse (Can't write to or create math temp directory): (m_1,m_2,...,m_r)
the parabolic subgroup Failed to parse (Can't write to or create math temp directory): P_{(m_1,m_2,...,m_r)}
equals the Levi subgroup Failed to parse (Can't write to or create math temp directory): L_{(m_1,m_2,...m_r)}

.