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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