Reductive IAPS

From Apstheory

[edit] Definition

[edit] 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.

[edit] 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)}

.