0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Rene
Vivi
JordanAdd your answer:
Earn +20 pts
What is an alternating group?
In group theory, an alternating group is a group of even permutations of a finite set.
How to write numbers in index form?
Writing Numbers in Index FormWe know that: So, we can write 8 as 23.Likewise, 27 can be written as 33and 125 can be written as 53.So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.Example 20Write 200 in simplest index form.Solution:Key Termsimplest index form
Describe McGregor's Theory X and Theory Y assumptions about workers?
Theory X is a group of ideas created by Douglas McGreggor in the 1960's. It deals with human motivations. He also discussed theory
When did Galois write about group theory?
Evariste Galois lived from 1811 till 1832. He died in a duel in Mary of 1832. He did not study mathematics at all until 1827 and appears to have concentrated on group theory in 1832.
What the uses of index number in index index?
uses of index
