10: Normal Subgroups and Factor Groups
( \newcommand{\kernel}{\mathrm{null}\,}\)
If H is a subgroup of a group G, then right cosets are not always the same as left cosets; that is, it is not always the case that gH=Hg for all g∈G. The subgroups for which this property holds play a critical role in group theory—they allow for the construction of a new class of groups, called factor or quotient groups. Factor groups may be studied directly or by using homomorphisms, a generalization of isomorphisms. We will study homomorphisms in Chapter 11.