Conjugacy: Difference between revisions
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In [[group theory]], '''conjugacy''' is the relation between elements of a group that states that one element is the [[conjugate]] of the other. This relation is an [[equivalence relation]], and the [[equivalence class]]es are the '''conjugacy classes''' of the group. | In [[group theory]], '''conjugacy''' is the relation between elements of a group that states that one element is the [[conjugate]] of the other. This relation is an [[equivalence relation]], and the [[equivalence class]]es are the '''conjugacy classes''' of the group. | ||
Another way of stating this is to say that conjugation is [[group action]] of ''G'' on itself, and the conjugacy classes are the [[orbit]]s of this action. | |||
The '''conjugacy problem''' is the [[decision problem]] of determining from a [[presentation of a group]] whether two elements of the group are conjugate . | The '''conjugacy problem''' is the [[decision problem]] of determining from a [[presentation of a group]] whether two elements of the group are conjugate . | ||
The conjugacy problem was identified by [[Max Dehn]] in 1911 as one of three fundamental decision problems in group theory; the other two being the [[group isomorphism problem]] and the [[word problem]]. | The conjugacy problem was identified by [[Max Dehn]] in 1911 as one of three fundamental decision problems in group theory; the other two being the [[group isomorphism problem]] and the [[word problem]]. | ||
Revision as of 14:25, 15 November 2008
In group theory, conjugacy is the relation between elements of a group that states that one element is the conjugate of the other. This relation is an equivalence relation, and the equivalence classes are the conjugacy classes of the group.
Another way of stating this is to say that conjugation is group action of G on itself, and the conjugacy classes are the orbits of this action.
The conjugacy problem is the decision problem of determining from a presentation of a group whether two elements of the group are conjugate .
The conjugacy problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the group isomorphism problem and the word problem.