Saturated APS relation

From Apstheory

[edit] Definition

An APS relation Failed to parse (Can't write to or create math temp directory): R

on an APS Failed to parse (Can't write to or create math temp directory): (G,\\Phi)
is termed saturated if whenever Failed to parse (Can't write to or create math temp directory): \\Phi_{m,n}(a,c)
is related to Failed to parse (Can't write to or create math temp directory): \\Phi_{m,n}(b,d)
then Failed to parse (Can't write to or create math temp directory): a
is related to Failed to parse (Can't write to or create math temp directory): b
(via Failed to parse (Can't write to or create math temp directory): R_m

) and Failed to parse (Can't write to or create math temp directory): c

is related to Failed to parse (Can't write to or create math temp directory): d
(via Failed to parse (Can't write to or create math temp directory): R_n

).

[edit] For groups

The left congruence or right congruence induced by a sub-APS of an APS of groups is saturated if and only if the sub-APS itself is saturated.