Quotient group

| 🗖 nosplit | ↑ parent "Subgroup" | 45, 916, 10

🗖 nosplit | ⇓ toc | ↑ parent "Subgroup" | Wikipedia | 45, 916, 10

Ultimate explanation: https://math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Does not have to be isomorphic to a subgroup:

This is one of the reasons why the analogy between simple groups of finite groups and prime numbers is limited.

Table of contents | 45, 916, 10
- 1. Subquotient | 64 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 2. Relationship between the quotient group and direct products | 304 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 3. Normal subgroup | 143, 503, 7 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
  - 3.1. Simple group | 48 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
  - 3.2. Classification of finite groups | 71, 312, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
    - 3.2.1. Classification of simple finite groups | 86, 133, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"
    - 3.2.2. Group extension problem | 108 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"

Ancestors

Subgroup | 0, 916, 12
Group | 0, 2k, 47
Algebra | 0, 2k, 65
Mathematics | 17, 10k, 239
Ciro Santilli's Homepage | 238, 147k, 2k

Incoming links

Fundamental theorem on homomorphisms | 29
Normal subgroup | 143, 503, 7
Relationship between the quotient group and direct products | 304