Some p-groups with two generators which satisfy certain conditions arising from arithmetic in imaginary quadratic fields

スポンサーリンク

概要

• 論文の詳細を見る

• Let p be an odd prime. We give a list of certain types of p-groups G with two generators which satisfy the following two conditions (A) and (B): (A) [Ker V<SUB>G→H</SUB>: [G, G]]=[G:H] for the transfer homomorphism V<SUB>G→H</SUB>: G→H/[H, H] of G to every normal subgroup H with cyclic quotient G/H, and (B) there exists an automorphism φ of G of order 2 such that g<SUP>φ+1</SUP>∈[G, G] for every g∈G. These conditions are necessary for G to be the Galois group of the second p-class field of an imaginary quadratic field. The list contains such a group that it may be useful for us to find an imaginary quadratic field with an interesting property on the capitulation problem.

• 東北大学の論文
• 1992-09-00

著者

• Miyake Katsuya

  Department Of Mathematical Sciences School Of Science And Engineering Waseda University

関連論文

• A Note on the Field Isomorphism Problem of X3+sX+s and Related Cubic Thue Equations
• On the field intersection problem of generic polynomials : a survey (Algebraic Number Theory and Related Topics 2007)
• Leopoldt kernels and central extensions of algebraic number fields
• Did Fermat See These Structures?
• On nilpotent extensions of algebraic number fields I
• Teiji Takagi, Founder of the Japanese School of Modern Mathematics
• On the units of an algebraic number field
• Some p-groups with two generators which satisfy certain conditions arising from arithmetic in imaginary quadratic fields
• A note on the field isomorphism problem of X^3 + sX + s and related cubic thue equations (Japan-Korea joint seminar on number theory and related topics 2008)

スポンサーリンク