G is a group, ω is a non -empty collection. Each element g in G corresponds to a mapping of ω: x → xg, x ∈ω, if satisfying: ①; ② xe = x (E is a unit element of G) Essence The adequate necessary conditions for G’s acting on ω are a replacement group on ω. I set G is a replacement group on ω, and H is a replacement group on γ. If there is one -to -one correspondence on ω to γ, and the one -to -one correspondence on G to H, the replacement G in any point α and G in the ω have
Then G and H are called replacement homogeneous. The replacement group of the two replacements must be homogeneous. But the replacement group of the same structure is not necessarily replacement of homogeneous. If ω and γ are set N yuan, then SΩ and sг are replaced with homogeneous. Therefore, the N yuan symmetrical group is homogeneous with SN. ω ω is a replacement on ω. If some points in ω make and σ keep the rest of the omega, then σ is called a rotation, which is recorded (α1, α2, αs, αs αs To. If the two rotations have no public changes, these two rotations are not intersecting. Each replacement can be the product that does not intersect the rotation, which is called the replacement rotation representation method, and except for the order of the rotation in the representation, the replacement rotation representation is unique.
G is a group, ω is a non -empty collection. Each element g in G corresponds to a mapping of ω: x → xg, x ∈ω, if satisfying:
①;
② xe = x (E is a unit element of G) Essence The adequate necessary conditions for G’s acting on ω are a replacement group on ω.
I set G is a replacement group on ω, and H is a replacement group on γ. If there is one -to -one correspondence on ω to γ, and the one -to -one correspondence on G to H, the replacement G in any point α and G in the ω have
Then G and H are called replacement homogeneous. The replacement group of the two replacements must be homogeneous. But the replacement group of the same structure is not necessarily replacement of homogeneous.
If ω and γ are set N yuan, then SΩ and sг are replaced with homogeneous. Therefore, the N yuan symmetrical group is homogeneous with SN.
ω ω is a replacement on ω. If some points in ω make
and σ keep the rest of the omega, then σ is called a rotation, which is recorded (α1, α2, αs, αs αs To. If the two rotations have no public changes, these two rotations are not intersecting. Each replacement can be the product that does not intersect the rotation, which is called the replacement rotation representation method, and except for the order of the rotation in the representation, the replacement rotation representation is unique.