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Two elements a and b of a group G are said to be CONJUGATE if there exists g in G such that [tex]a=gbg^{-1}[/tex].

For instance, show that all elements in the symmetric group S5 of order 6 conjugate.

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- Thread starter Treadstone 71
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Two elements a and b of a group G are said to be CONJUGATE if there exists g in G such that [tex]a=gbg^{-1}[/tex].

For instance, show that all elements in the symmetric group S5 of order 6 conjugate.

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matt grime

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EDIT: Yes, that's the correct definition, as well.

Again, do it: take an element of order 6, compute its conjugates with a couple of elements and see who to generate all elements of order 6.

Eg, in S_n n>2, consider (12)(23)(12)=(13), thus it's clear that all elements of order 2 are conjugate

Again, do it: take an element of order 6, compute its conjugates with a couple of elements and see who to generate all elements of order 6.

Eg, in S_n n>2, consider (12)(23)(12)=(13), thus it's clear that all elements of order 2 are conjugate

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matt grime

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