The 4-class group of real quadratic number fields

2013/10/24 by Lemmermeyer, Franz
#11R37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1310.6607

Abstract

In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire's result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank at least 4, using a technique due to F. Hajir.

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