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Dear Gap Forum,

Marco Costantini asked:

let p be a fixed prime, let G be a finite p-group (but the following makes sense for every gruop), and let \mho_i(G) and \mho_{(i)}(G) the subgroups of G defined by \mho_i(G) := the subgroup generated by the p^i-powers of the elements of G, \mho_{(0)}(G) := G, \mho_{(i+1)}(G) := \mho_1(\mho_{(i)}(G)).Is there a simple method in gap to calculate

the subgroups \mho_i(G) and \mho_{(i)}(G)?

In GAP4b4 there is a command:

Agemo(<G>,<p>,<i>)

that computes \mho_i(G) (for the prime $p$). There is so far no command for

\mho_{(i)}. The following recursive GAP4 function implements the

definition, so it is probably not the most efficient way for the

computation, but might at least work for smaller groups.

BracketAgemo:=function(G,p,i)

if i=0 then

return G;

else

return Agemo(BracketAgemo(G,p,i-1),p,1);

fi;

end;

I hope this is of help.

Alexander Hulpke

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