Commutator relations and the clones of finite groups
by
Jason Shaw
University of Colorado

If G is a group, then the clone of G, denoted Clo(G), is the set of finitary operations on G which are the interpretations of group words. It is of interest to ask: Does there exists an integer k > 0 such that for all groups G, Clo(G) is determined by the subgroups of G^k? By determined we mean that an operation f is in Clo(G) if and only if f preserves the subgroups of G^k. In this presentation we show that there does not exist k > 0 such that for all finite groups G, Clo(G) is determined by the subgroups of G^k.

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Date received: June 18, 2008