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Quotient group

| 🗖 nosplit | ↑ parent "Subgroup" | words: 51 | descendant words: 977 | descendants: 11

🗖 nosplit | ⇓ toc | ↑ parent "Subgroup" | Wikipedia | words: 51 | descendant words: 977 | descendants: 11

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 | 51, 977, 11
- 1. Subquotient | 64 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 2. Relationship between the quotient group and direct products | 308 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 3. Normal subgroup | 149, 554, 8 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
  - 3.1. Simple group | 48 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
  - 3.2. Classification of finite groups | 77, 357, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
    - 3.2.1. Classification of finite simple groups | 88, 170, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"
    - 3.2.2. Group extension problem | 110 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"

Ancestors

Subgroup | 0, 977, 13
Group | 0, 1k, 33
Algebra | 0, 2k, 62
Mathematics | 17, 13k, 336
Ciro Santilli's Homepage | 262, 182k, 3k

Incoming links

Fundamental theorem on homomorphisms | 31
Normal subgroup | 149, 554, 8
Relationship between the quotient group and direct products | 308