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Start Over Topic elliptic curves Journal transactions of the american mathematical society, series b Database Academic Search Index Publisher american mathematical society

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1. A group theoretic perspective on entanglements of division fields.

Author

Daniels, Harris B. and Morrow, Jackson S.

Subjects
*ELLIPTIC curves, *DIVISION algebras, *FINITE groups
Abstract

In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer n and a subgroup G\subseteq GL_2(\mathbb {Z}/n\mathbb {Z}) with surjective determinant, we provide a definition for G to represent an (a,b)-entanglement and give additional criteria for G to represent an explained or unexplained (a,b)-entanglement. Using these new definitions, we determine the tuples ((p,q),T), with p

Published
2022
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