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Concept
Commutator Subgroup
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Summary
The
Commutator Subgroup
, also known as the
Derived subgroup
, is the subgroup generated by all commutators of a group, capturing the essence of how non-abelian a group is. It plays a crucial role in understanding the
Structure of a group
, as it is the
Smallest normal subgroup
for which the
Quotient Group
is abelian, reflecting the group's 'abelianization'.
Concepts
Group Theory
Normal Subgroup
Commutator
Abelian Group
Quotient Group
Group Homomorphism
Derived Series
Solvable Group
Perfect Group
Nilpotent Group
Upper Central Series
Central Series
Lower Central Series
Relevant Degrees
Algebra 100%
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