HAP home
 Top of Book   Previous Chapter   Next Chapter 

18. Cat-1-groups

18. Cat-1-groups

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.


 


 Top of Book   Previous Chapter   Next Chapter 
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Ind

generated by GAPDoc2HTML