Motivation For Definition
The reason G/N is called a quotient group comes from division of integers. When dividing 12 by 3 one obtains the answer 4 because one can regroup 12 objects into 4 subcollections of 3 objects. The quotient group is the same idea, however we end up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects.
To elaborate, when looking at G/N with N a normal subgroup of G, the group structure is used to form a natural "regrouping". These are the cosets of N in G. Because we started with a group and normal subgroup the final quotient contains more information than just the number of cosets (which is what regular division yields), but instead has a group structure itself.
Read more about this topic: Quotient Group
Famous quotes containing the words motivation for, motivation and/or definition:
“Self-determination has to mean that the leader is your individual gut, and heart, and mind or we’re talking about power, again, and its rather well-known impurities. Who is really going to care whether you live or die and who is going to know the most intimate motivation for your laughter and your tears is the only person to be trusted to speak for you and to decide what you will or will not do.”
—June Jordan (b. 1939)
“Self-determination has to mean that the leader is your individual gut, and heart, and mind or we’re talking about power, again, and its rather well-known impurities. Who is really going to care whether you live or die and who is going to know the most intimate motivation for your laughter and your tears is the only person to be trusted to speak for you and to decide what you will or will not do.”
—June Jordan (b. 1939)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)