Generalising a result of Brown and Loday, we give for n=3 and 4, a decomposition of the group, d_nNG_n, of boundaries of a simplicial group G as a product of commutator subgroups. Partial results are given for higher dimensions. Applications to 2-crossed modules and quadratic modules are discussed.
Please note the electronically available References at
http://www.tac.mta.ca/tac/volumes/1998/n7/reference.html
Theory and Applications of Categories, Vol. 4, 1998, No. 7, pp 148-173 http://www.tac.mta.ca/tac/volumes/1998/n7/n7.dvi http://www.tac.mta.ca/tac/volumes/1998/n7/n7.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1998/n7/n7.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1998/n7/n7.ps