کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771669 | 1630421 | 2018 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Counting Hopf-Galois structures on cyclic field extensions of squarefree degree
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate Hopf-Galois structures on a cyclic field extension L/K of squarefree degree n. By a result of Greither and Pareigis, each such Hopf-Galois structure corresponds to a group of order n, whose isomorphism class we call the type of the Hopf-Galois structure. We show that every group of order n can occur, and we determine the number of Hopf-Galois structures of each type. We then express the total number of Hopf-Galois structures on L/K as a sum over factorisations of n into three parts. As examples, we give closed expressions for the number of Hopf-Galois structures on a cyclic extension whose degree is a product of three distinct primes. (There are several cases, depending on congruence conditions between the primes.) We also consider one case where the degree is a product of four primes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 493, 1 January 2018, Pages 1-19
Journal: Journal of Algebra - Volume 493, 1 January 2018, Pages 1-19
نویسندگان
Ali A. Alabdali, Nigel P. Byott,