Natural Central Extensions of Groups

Details Natural Central Extensions of Groups Natural Central Extensions of Groups

2005-05-13

arxiv.org/abs/math/0505285v2

Groups Geom. Dyn. 2, 245-261 (2008)

Mathematics

Group Theory

13 pages, completely rewritten version

Scientific paper

Given a group $G$ and an integer $n\geq2$ we construct a new group $\tilde{{\cal K}}(G,n)$. Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cover by a kind of warped Baer sum.

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