What is a group homomorphism?
Understand the Problem
The question refers to the concept of a group homomorphism in abstract algebra, which is a structure-preserving map between two algebraic structures, specifically groups. The focus appears to be on the definition and properties of homomorphisms as they relate to group theory.
Answer
A function between two groups that preserves the group operation.
A group homomorphism is a function between two groups that preserves the group operation.
Answer for screen readers
A group homomorphism is a function between two groups that preserves the group operation.
More Information
Group homomorphisms help us understand the algebraic structure of groups and their relationships.
Tips
Common mistakes include not verifying the preservation of the group operation for all elements or misunderstanding the operations involved.
Sources
- Group Homomorphism -- from Wolfram MathWorld - mathworld.wolfram.com
- Group homomorphism - Wikipedia - en.wikipedia.org
- Group Homomorphisms - Abstract Algebra - YouTube - youtube.com
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