The p-adic group ring of SL2(p f)

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In the present article we show that the Zp[ζpf-1]-order Zp[ζpf-1]SL2(pf) can be recognized among those orders whose reduction modulo p is isomorphic to FpfSL2(pf) using only ring-theoretic properties. In other words we show that FpfSL2(pf) lifts uniquely to a Zp[ζpf-1]-order, provided certain reasonable conditions are imposed on the lift. This proves a conjecture made by Nebe in [8] concerning the basic order of Z2[ζ2f-1]SL2(2f).

Original languageEnglish
Pages (from-to)421-459
Number of pages39
JournalJournal of Algebra
Publication statusPublished - 15 Jul 2014


  • Derived equivalences
  • Integral representations
  • Orders


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