Geodesic
Kummer theory on the product of an elliptic curve by the multiplicative group
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 83-88

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This note extends classical results on certain Galois groups attached to onedimensional algebraic groups. We prove that the fields arising from the division of a fixed set of rational points on the product of an elliptic curve by the multiplicative group are as “large” as possible. 
Bertrand, D. Kummer theory on the product of an elliptic curve by the multiplicative group. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 83-88. doi: 10.1017/S001708950000450X
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