7.54 IsConjugate

IsConjugate( G, x, y )

Let x and y be elements of the parent group of G. Then IsConjugate returns true if x is conjugate to y under an element g of G and false otherwise.

    gap> s5 := Group( (1,2,3,4,5), (1,2) );
    Group( (1,2,3,4,5), (1,2) )
    gap> a5 := Subgroup( s5, [ (1,2,3), (2,3,4), (3,4,5) ] );
    Subgroup( Group( (1,2,3,4,5), (1,2) ), [ (1,2,3), (2,3,4), (3,4,5) ] )
    gap> IsConjugate( a5, (1,2,3,4,5), (1,2,3,4,5)^2 );
    false
    gap> IsConjugate( s5, (1,2,3,4,5), (1,2,3,4,5)^2 );
    true 

The default function GroupOps.IsConjugate uses Representative (see Representative) in order to check whether x is conjugate to y under G.

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