کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4586690 | 1334110 | 2009 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A polynomial-time reduction algorithm for groups of semilinear or subfield class
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
We present a Las Vegas algorithm for finding a nontrivial reduction of groups that are irreducible with m generators and either lie in the subfield class of matrix or projective groups or are semilinear or have non-absolutely irreducible derived group. Let RA denote the cost of producing a random element from a matrix algebra A and R〈HG〉 denote the cost of producing a random element in the normal closure of a group H by a group G. Then the algorithm runs in O(d3(m+dloglogdlogq)+RAlog(logd)+R〈HG〉dlogq) finite field operations. We also characterise the absolutely irreducible groups G over arbitrary fields whose derived group consists only of scalars, and prove probabilistic generation results about matrix groups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 322, Issue 3, 1 August 2009, Pages 613-637
Journal: Journal of Algebra - Volume 322, Issue 3, 1 August 2009, Pages 613-637