Splitting of Clifford groups associated to finite abelian groups
Abstract
The Clifford group associated with a finite abelian group gives rise to a natural extension by the corresponding symplectic group. We prove that this extension splits as a semidirect product if and only if the group order is not divisible by four. This confirms a conjecture of Korbel\'ar and Tolar and extends their cyclic result to arbitrary finite abelian groups.
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