A homogeneous group is a set together with a map satisfying:
for all .
A map of homogeneous groups is a homomorphism if it , for all .
A non-empty homogeneous group is essentially a group, as given any , we may define the following product on :
One may recover a homogeneous group from a group obtained this way, by setting
Also, every group may be obtained from a homogeneous group.
Homogeneous groups are homogeneous: Given we have a homomorphism taking to , given by .
|Date of creation||2013-03-22 16:12:12|
|Last modified on||2013-03-22 16:12:12|
|Last modified by||whm22 (2009)|
|Defines||homomorphism of homogeneous groups|