TY - JOUR

T1 - On Two Group Functors Extending Schur Multipliers

AU - Dietrich, Heiko

AU - Moravec, Primož

PY - 2020/8/26

Y1 - 2020/8/26

N2 - 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.

AB - 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.

KW - Finite groups

KW - non-abelian exterior square

KW - Schur multiplier

UR - http://www.scopus.com/inward/record.url?scp=85089784601&partnerID=8YFLogxK

U2 - 10.1080/10586458.2020.1796857

DO - 10.1080/10586458.2020.1796857

M3 - Article

AN - SCOPUS:85089784601

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

ER -