Saturated sub-APS
From Apstheory
A sub-APS Failed to parse (Can't write to or create math temp directory): H
of an APS Failed to parse (Can't write to or create math temp directory): (G,\\Phi) is termed a saturated sub-APS if for any Failed to parse (Can't write to or create math temp directory): (m,n)
, the inverse image via Failed to parse (Can't write to or create math temp directory): \\Phi_{m,n}
of Failed to parse (Can't write to or create math temp directory): H_{m+n} is precisely Failed to parse (Can't write to or create math temp directory): H_m × Failed to parse (Can't write to or create math temp directory): H_n
.
For an APS Failed to parse (Can't write to or create math temp directory): G
of groups with a sub-APS Failed to parse (Can't write to or create math temp directory): H
, the following are equivalent:
- Failed to parse (Can't write to or create math temp directory): H
is a saturated sub-APS of Failed to parse (Can't write to or create math temp directory): G
.
- The left congruence induced by Failed to parse (Can't write to or create math temp directory): H
is a saturated APS relation.
- The coset space APS of Failed to parse (Can't write to or create math temp directory): H
in Failed to parse (Can't write to or create math temp directory): G is an IAPS (of sets)
Further, the following are equivalent:
- Failed to parse (Can't write to or create math temp directory): H
is a saturated normal sub-APS of Failed to parse (Can't write to or create math temp directory): G
.
- The congruence induced by Failed to parse (Can't write to or create math temp directory): H
is a saturated APS congruence.
- The quotient APS is an IAPS of groups.