On Two Group Functors Extending Schur Multipliers

Heiko Dietrich, Primož Moravec

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Liedtke has introduced group functors K and (Formula presented.), 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 (Formula presented.) to a group functor τ arising in the construction of the non-abelian exterior square of a group. In contrast to (Formula presented.), there exist efficient algorithms for constructing τ, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when (Formula presented.) is a quotient of (Formula presented.), and when (Formula presented.) and (Formula presented.) are isomorphic.

Original languageEnglish
Number of pages13
JournalExperimental Mathematics
Publication statusAccepted/In press - 26 Aug 2020


  • Finite groups
  • non-abelian exterior square
  • Schur multiplier

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