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Original Articles

Quotient Graphs and Amalgam Presentations for Unitary Groups Over Cyclotomic Rings

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Pages 191-217 | Published online: 08 Aug 2021
 

Abstract

Suppose 4|n,n8, F=Fn=Q(ζn+ζ¯n), and there is one prime p=pn above 2 in Fn. We study amalgam presentations for PU2(Z[ζn,1/2]) and PSU2(Z[ζn,1/2]) with the Clifford-cyclotomic group in quantum computing as a subgroup. These amalgams arise from an action of these groups on the Bruhat-Tits tree Δ=Δp for SL2(Fp) constructed via the Hamilton quaternions. We explicitly compute the finite quotient graphs and the resulting amalgams for 8n48,n44, as well as for PU2(Z[ζ60,1/2]).

2010 Mathematics Subject Classification.:

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