Establishing the minimal index in a parametric family of bicyclic biquadratic fields

Let c ≥ 3 be a positive integer such that c, 4c + 1, c − 1 are square-free integers relatively prime in pairs. In this paper we find the minimal index and determine all elements with minimal index in the bicyclic biquadratic field K = ℚ(√(4c + 1)c, √(c − 1)c). The author was supported by the Ministry of Science, Education and Sports, Republic of Croatia, grant 037-0372781-2821.