25.32 RefinedAgSeries

RefinedAgSeries( G )

RefinedAgSeries returns a new parent group isomorphic to a parent group G with a PAG series, if the ag group G has only an AG series.

Note that in the case that G has a PAG series, G is returned without any further action.

The names of the new generators are constructed as follows. Let (g_1,..., g_n) be the AG system of the ag group G and n(g_i) the name of g_i. If the relative order of g_i is a prime, then n(g_i) is the name of a new generator. If the relative order is a composite number with r prime factors, then there exist r new generators with names n(g_i)_1, ..., n(g_i)_r.

    gap> c12 := AbstractGenerator( "c12" );;
    gap> F := rec( generators := [ c12 ],
    >              relators   := [ c12 ^ ( 2 * 2 * 3 ) ] );
    rec(
      generators := [ c12 ],
      relators := [ c12^12 ] )
    gap> G := AgGroupFpGroup( F );
    #W  AgGroupFpGroup: composite index, use 'RefinedAgSeries'
    Group( c12 )
    gap> RefinedAgSeries( G );
    Group( c121, c122, c123 ) 

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