Abstract
Liedtke has introduced group functors K and , which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions and Schur multipliers. In this work, we relate K and to a group functor τ arising in the construction of the non-abelian exterior square of a group. In contrast to , there exist efficient algorithms for constructing τ, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when is a quotient of , and when and are isomorphic.
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