> < ^ Date: Thu, 18 Nov 1999 23:16:25 +0100 (MET)
> < ^ From: Laurent Bartholdi <Laurent.Bartholdi@math.unige.ch >
> ^ Subject: powers and roots

hullo, dear little taxpayers,
i wondered how one can compute isolators in gap.
recall the isolator of a subgroup H of G is
{x in G | x^n in H for some n}
there is also an interesting series of normal subgroups G_n of G,
where G_n=isolator of gamma_n(G), and {gamma_n} is the LCS.

it is known that G_n is Delta^n cap G, where Delta in the augmontation
ideal in the group algebra QG. i'm not sure that helps.

also, given a subgroup H of G and an integer n, how does one compute the
subgroup of H generated by nth powers of elements in H?

all my groups will be infinite but of finite index in a f.p. group.
they're also residually finite, so it could work (as second best choice)
to work in large enough finite quotients.

thanks in advance,
laurent

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