Metacommutation of Hurwitz primes

Cohn, Henry; Kumar, Abhinav

doi:10.1090/S0002-9939-2014-12358-6

Metacommutation of Hurwitz primes
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by Henry Cohn and Abhinav Kumar PDF

Proc. Amer. Math. Soc. 143 (2015), 1459-1469

Abstract:

Conway and Smith introduced the operation of metacommutation for pairs of primes in the ring of Hurwitz integers in the quaternions. We study the permutation induced on the primes of norm $p$ by a prime of norm $q$ under metacommutation, where $p$ and $q$ are distinct rational primes. In particular, we show that the sign of this permutation is the quadratic character of $q$ modulo $p$.

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