24.8 RelativeOrder

RelativeOrder( g )

RelativeOrder returns the relative order of an ag word g as integer.

Let G be the parent group of g and G=G_0 > ... > G_n={1} the AG series of G. Let delta be the maximal positive integer such that g is an element of G_{delta-1}. The relative order of g is the index of G_{delta+1} in G_delta, that is the order of the factor group G_delta/G_{delta+1}.

If g is the identity 1 is returned.

Note that RelativeOrder allows records that mimic agwords as arguments.

    gap> RelativeOrder( a );
    2
    gap> RelativeOrder( b );
    3
    gap> RelativeOrder( b^2 * c * d );
    3 

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