### Abstract

Following the analogies between knots and primes, we introduce arithmetic analogues of higher linking matrices for prime numbers by using the arithmetic Milnor numbers. As an application, we describe the Galois module structure of the l-class group of a cyclic extension of ℚ of degree l (l being a prime number) in terms of the arithmetic higher linking matrices. In particular, our formula generalizes the classical formula of Rédei on the 4 and 8 ranks of the 2-class group of a quadratic field.

Original language | English |
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Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 669-683 |

Number of pages | 15 |

DOIs | |

Publication status | Published - Jan 1 2008 |

### Publication series

Name | Progress in Mathematics |
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Volume | 265 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Morishita, M. (2008). Milnor invariants and l-class groups. In

*Progress in Mathematics*(pp. 669-683). (Progress in Mathematics; Vol. 265). Springer Basel. https://doi.org/10.1007/978-3-7643-8608-5_16