A black-box group algorithm for recognizing finite symmetric and alternating groups, I
نویسندگان
چکیده
منابع مشابه
A Black-box Group Algorithm for Recognizing Finite Symmetric and Alternating Groups, I
We present a Las Vegas algorithm which, for a given black-box group known to be isomorphic to a symmetric or alternating group, produces an explicit isomorphism with the standard permutation representation of the group. This algorithm has applications in computations with matrix groups and permutation groups. In this paper, we handle the case when the degree n of the standard permutation repres...
متن کاملQuantum Algorithm for Decomposing Black-Box Finite Abelian Groups
Cheung and Mosca [1] gave an efficient quantum algorithm for decomposing finite abelian groups in a unique-encoding group model. We present another efficient quantum algorithm for this problem in a more general model, the black-box group model, where each group element is not necessarily uniquely encoded.
متن کاملNormal coverings of finite symmetric and alternating groups
In this paper we investigate the minimum number of maximal subgroups Hi, i = 1 . . . k of the symmetric group Sn (or the alternating group An) such that each element in the group Sn (respectively An) lies in some conjugate of one of the Hi. We prove that this number lies between aφ(n) and bn for certain constants a, b, where φ(n) is the Euler phi-function, and we show that the number depends on...
متن کاملThe Subgroup Structure of Finite Alternating and Symmetric Groups
In this course we will be studying the subgroup structure of the finite alternating and symmetric groups. What does the phrase “study the subgroups of symmetric groups” mean? In this introduction I’ll suggest an answer to that question, and attempt to convince you that answer has some merit. In the process you’ll get some idea of the material we will be covering, and I’ll attempt to motivate th...
متن کاملfinite groups which are the products of symmetric or alternating groups with $l_3(4)$
in this paper, we determine the simple groups $g=ab$, where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$, letters.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03040-x