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 | | But the direct limit of this system is defined to be G_w which has order 2, and then G_{w+1} = 1, which of course has trivial centre. |
 | | In the example, each G_i = is mapped to G_{i+1} by a->a^2, b->b, and the direct limit is essentially the subgroup {1,b}, because a -> a^2 -> a^4 = 1 dies. |
 | | In general, centres of each individual G_i map onto 1 in the direct limit, but that does nor mean that the direct limit has no centre. |
| www.math.niu.edu /~rusin/known-math/01_incoming/aut_tower (788 words) |
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