AutomorphismGroupAsCatOneGroup(G)
Inputs a group G and returns the Cat-1-group C corresponding th the crossed module G-> Aut(G). |
HomotopyGroup(C,n)
Inputs a cat-1-group C and an integer n. It returns the nth homotopy group of C. |
HomotopyModule(C,2)
Inputs a cat-1-group C and an integer n=2. It returns the second homotopy group of C as a G-module (i.e. abelian G-outer group) where G is the fundamental group of C. |
ModuleAsCatOneGroup(G,alpha,M)
Inputs a group G, an abelian group M and a homomorphism alpha: G-> Aut(M). It returns the Cat-1-group C corresponding th the zero crossed module 0: M-> G. |
MooreComplex(C)
Inputs a cat-1-group C and returns its Moore complex [M_1 -> M_0] as a list whose single entry is a homomorphism of groups. |
NormalSubgroupAsCatOneGroup(G,N)
Inputs a group G with normal subgroup N. It returns the Cat-1-group C corresponding th the inclusion crossed module N-> G. |
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