| GOuterGroup(E,N)GOuterGroup()Inputs a group E and normal subgroup N. It returns N as a G-outer group where G=E/N. The function can be used without an argument. In this case an empty outer group C is returned. The components must be set using SetActingGroup(C,G), SetActedGroup(C,N) and SetOuterAction(C,alpha). | 
| GOuterGroupHomomorphismNC(A,B,phi)GOuterGroupHomomorphismNC()Inputs G-outer groups A and B with common acting group, and a group homomorphism phi:ActedGroup(A) --> ActedGroup(B). It returns the corresponding G-outer homomorphism PHI:A--> B. No check is made to verify that phi is actually a group homomorphism which preserves the G-action. The function can be used without an argument. In this case an empty outer group homomorphism PHI is returned. The components must then be set. | 
| GOuterHomomorphismTester(A,B,phi)Inputs G-outer groups A and B with common acting group, and a group homomorphism phi:ActedGroup(A) --> ActedGroup(B). It tests whether phi is a group homomorphism which preserves the G-action. The function can be used without an argument. In this case an empty outer group homomorphism PHI is returned. The components must then be set. | 
| Centre(A)Inputs G-outer group A and returns the group theoretic centre of ActedGroup(A) as a G-outer group. | 
| DirectProductGog(A,B)DirectProductGog(Lst)Inputs G-outer groups A and B with common acting group, and returns their group-theoretic direct product as a G-outer group. The outer action on the direct product is the diagonal one. The function also applies to a list Lst of G-outer groups with common acting group. For a direct product D constructed using this function, the embeddings and projections can be obtained (as G-outer group homomorphisms) using the functions Embedding(D,i) and Projection(D,i). | 
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