On the Free Polygroups and Crossed Polymodules

The concept crossed module was introduced by J. H. C. Whitehead in his work on combinatorial homotopy theory. Crossed modules and its applications playvery important roles in category theory, homology and cohomology of groups, homo- topy theory, algebra, ktheory etc. Actor crossed module of algebroid was de ned byM. Alp. Nilpotent, Solvable, n-Complete and Representations of crossed modules was studied by M. A. Dehghanizadeh and B. Davvaz. In this paper, we suppose that P bea free polygroup, and (C; P; @; ) be a P-crossed polymodule or a non-aspherical projec- tive P-crossed polymodule or a residually nilpotent non-aspherieal projective P-crossed polymodule and we got the structur Coker(@).

کلیدواژه ها:

Crossed module ، Crossed polymodule ، Free polygroup