A note on the probability of generating alternating or symmetric groups
نویسندگان
چکیده
منابع مشابه
Asymptotics of Generating the Symmetric and Alternating Groups
The probability that a random pair of elements from the alternating group An generates all of An is shown to have an asymptotic expansion of the form 1¡1/n¡ 1/n2¡4/n3¡23/n4¡171/n5¡ ... . This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group Sn generates either An or Sn. Similar results hold for the case of r generators (r > 2). MSC 2...
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 کاملGenerating Symmetric and Alternating Groups with Elements of Fixed Order
Many of the commonly-used generating sets for the symmetric group Σn and the alternating group An either consist of a number of generators that grows as n grows or else contain an element whose order grows as n grows. For instance, Σn is generated by the set of adjacent transpositions, and it is also generated by a single transposition along with an n-cycle. Similarly, An is generated by all 3-...
متن کاملA NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کاملfinite simple 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: Archiv der Mathematik
سال: 2015
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-015-0796-8