Maximal Factor of A Minimal Set

Lei (x ,t) be a minimal transformation group and let !p be a homomorphism of(x ,t). we willfind a maximal factor of (x ,t) with respect (o!p. that is, we will find a minimal transformationgroup (y ,t), an auto orphism 'fi : (y ,t ) --) (y ,t), and a homomorphism if : (x ,t) --) (y ,t),such that the following diagram commutesand for any minimal transformation group(z.t), and auto orphisml1 : (z.t) --) (z,t), andhornomorphism zz : (x ,t) --) (z ,t), with the following property:we will find a homomorphism if: (y ,t) --) (z ,t ) such that the following diagram commutes.that is, in general, the following diagram commutesthe minimal set (y ,t) with the authomorphism if/ is called a maximal [actor of the minimalset(x ,t ).