کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10130504 | 1645338 | 2018 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An algorithm to construct candidates to counterexamples to the Zassenhaus Conjecture
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
By results of Cliff and Weiss and Hertweck, Sehgal's Problem has a positive solution if N has at most one non-cyclic Sylow subgroup. We present some algorithms to study Sehgal's Problem when N has at most one non-abelian Sylow subgroup. They are based on the Cliff-Weiss inequalities introduced by the authors in a previous paper. With the help of these algorithms we obtain some positive answers to Sehgal's Problem and use them to show that for units in V(ZG,N) our method is strictly stronger than the well known HeLP Method. We then present a method to use the output of one of the algorithms to construct explicit metabelian groups which are candidates to a negative solution to Sehgal's Problem. Recently Eisele and Margolis showed that some of the examples proposed in this paper are indeed counterexamples to the Zassenhaus Conjecture. These are the first known counterexamples. Moreover, we prove that every metabelian negative solution of Sehgal's Problem satisfying some minimal conditions is given by our construction.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 514, 15 November 2018, Pages 536-558
Journal: Journal of Algebra - Volume 514, 15 November 2018, Pages 536-558
نویسندگان
Leo Margolis, Ángel del RÃo,