For a given finite group G, the problem whether there exist infinitely many number fields K with large class number and Galois group Gal(K/Q) ≌ G is interesting and important. This problem was proved affirmatively for some groups G. In this paper, we approach this problem by considering h_KR_K, where h_K is the class number of K and R_K is the regulator of K. We prove that there exist infinitely many bicubic number fields K with large h_KR_K. Moreover, we also prove generalization of the claim.
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机译：对于给定的有限组G，问题是否存在具有大类数和Galois Group Gal（K / Q）≌G的无限数量的数量k是有趣的，并且重要的。 对于某些组G，肯定地证明了这个问题。在本文中，我们通过考虑H_KR_K来接近这个问题，其中H_K是K和R_K的类数是K的稳压器。我们证明存在无限的双方数量k 大h_kr_k。 此外，我们还证明了索赔的概括。
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