What is a coset?
Understand the Problem
The question is asking for the definition and explanation of the mathematical concept 'coset', commonly discussed in group theory within the field of abstract algebra.
Answer
A subset of a group formed by multiplying all elements of a subgroup by a fixed element of the group.
The final answer is a subset of a group formed by multiplying all elements of a subgroup by a fixed element of the group.
Answer for screen readers
The final answer is a subset of a group formed by multiplying all elements of a subgroup by a fixed element of the group.
More Information
Cosets play a central role in group theory, helping classify and understand group structures, and are fundamental in the proof of Lagrange's theorem.
Tips
Avoid confusing cosets with subgroups; cosets are generally not subgroups themselves unless the fixed element is the identity element.
Sources
- Coset Definition & Meaning - Merriam-Webster - merriam-webster.com
- Coset -- from Wolfram MathWorld - mathworld.wolfram.com
- Cosets in Mathematics - GeeksforGeeks - geeksforgeeks.org
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