Let $h \geq 2$ be an integer and $F$ a formal group over $\mathbf{Z}_p$ of Honda type $p + X^h$. The aim of this paper is to calculate the index of the image of the norm of $F$ in the local cyclotomic fields by following Kobayashi's method ([1]). Here we use the property of certain subgroups which we call norm subgroups.
References
Kobayashi, S.: Iwasawa theory for elliptic curves at supersingular primes. Invent. Math., 152, 1–36 (2003). MR1965358 10.1007/s00222-002-0265-4 Kobayashi, S.: Iwasawa theory for elliptic curves at supersingular primes. Invent. Math., 152, 1–36 (2003). MR1965358 10.1007/s00222-002-0265-4
Kurihara, M.: On the Tate Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction I. Invent. Math., 149, 195–224 (2002). MR1914621 10.1007/s002220100206 Kurihara, M.: On the Tate Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction I. Invent. Math., 149, 195–224 (2002). MR1914621 10.1007/s002220100206
