Say we have a group G, and some subgroup H. The number of cosets of H in G is called the index of H in G. This is written [G:H].
If G and H are finite, [G:H] is just |G|/|H|.
What if they are infinite? Here is an example. Let G be the integers under addition. Let H be the even integers under addition, a subgroup. The cosets of H in G are H and H+1. H+1 is the set of all even integers + 1, so the set of all odd integers. Here we have partitioned the integers into two cosets, even and odd integers. So [G:H] is 2.
City Index Group's population is 600.
City Index Group was created in 1983.
Target Group Index was created in 2010-01.
what is mean by statistical approach and economical approach in the theory of index numbers?
In abstract algebra, group theory studies structures known as groups. Group theory has three historical sources number theory, the theory of algebraic equations, and geometry.
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