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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

E-Mail: mailto:Laurent.Bartholdi@m-a-t-h.unige.ch (delete hyphens) S-Mail: Laurent Bartholdi, 15 Bvd de la Cluse, 1205 Genève, Switzerland Office: #610B, 2-4 Rue du Lièvre, Case Postale 240, 1211 Genève 24, Switzerland Phones: +41 22 3280012 (Home) +41 22 7026947 (Office) +41 22 3002064 (Fax)

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