Platonic and alternating 2-groups

Narthana Epa, Nora Ganter

Abstract


We recall Schur’s work on universal central extensions and develop the anal-
ogous theory for categorical extensions of groups. We prove that the String 2-groups are
universal in this sense and study in detail their restrictions to the finite subgroups of the
Spin groups. Of particular interest are subgroups of the 3-sphere Spin(3), as well as the
spin double covers of the alternating groups, whose categorical extensions turn out to be
governed by the stable 3-stem π 3 (S 0 ).

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