I dont think it is a matter of dominance and influence with regards to a definition of racism, that inevitably feeds power.
The white girl calling her baristar neighbour a paki is damaging on a personal level but no more than that on the surface. however voicing that inherent view to friends, neighbours, her children normalsises the attidure that the asian man is all the things they belive him to be, therefore other asian men must also be. therefore it becomes ingraned in a society, passed through generations compounding stereo types.
So in the unfortunate case of stephen lawrence, victoria climbie, and many more, these views are generalised, some individual proffessionals, public servants, police officers, social workers, nursing staff are unable to differentate the individual with the stereotype and so systems fail individuals. That is where the power evolves as a result of dominance, because too often black and other ethnic minorities are well under represented.
very similar to how woman are in the work place etc, the one time dominance of males over females has taken a life time to combat.
and very possibly aslo true, smallwhitecat, of why people compalian about politicians coming from elite schools the dominance of that elite leads to the underrepresentation of others within society.