Jordan constants of quaternion algebras over number fields and simple abelian surfaces over fields of positive characteristic

Abstract

We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative subgroup of the endomorphism algebras of simple abelian surfaces over fields of positive characteristic.

Any comments will be appreciated. arXiv admin note: text overlap with arXiv:2002.05535, arXiv:1901.04470, arXiv:2002.12353, arXiv:1809.06251. Introduction is slightly modified according to thankful comments. One thing is fixed regarding the Jordan constant of the binary tetrahedral group