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2019 Subgroups of division rings
Mark Lewis, Murray Schacher
Rocky Mountain J. Math. 49(7): 2227-2251 (2019). DOI: 10.1216/RMJ-2019-49-7-2227

Abstract

We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders. Our results are highly dependent on the computer software package Magma, although alternatives would probably work fine. A computer approach is required because our results require a listing of all maximal orders; the sheer number of maximal orders grows exponentially quickly and determining them all is not obtainable in polynomial time. When discriminants are large enough, the determination of a single maximal order is also exponentially hard. We indicate the limits as these problems arise.

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Mark Lewis. Murray Schacher. "Subgroups of division rings." Rocky Mountain J. Math. 49 (7) 2227 - 2251, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2227

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152862
MathSciNet: MR4039967
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2227

Subjects:
Primary: 12E15, 16K20
Secondary: 16U60

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 7 • 2019
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