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Azizollah?AzadEmail author Mohammad?A.?Iranmanesh Cheryl?E.?Praeger Pablo?Spiga 《Journal of Algebraic Combinatorics》2011,34(4):683-710
In this paper we introduce and study a family An(q)\mathcal{A}_{n}(q) of abelian subgroups of GLn(q){\rm GL}_{n}(q) covering every element of GLn(q){\rm GL}_{n}(q). We show that An(q)\mathcal{A}_{n}(q) contains all the centralizers of cyclic matrices and equality holds if q>n. For q>2, we obtain an infinite product expression for a probabilistic generating function for |An(q)||\mathcal{A}_{n}(q)|. This leads to upper and lower bounds which show in particular that
c1q-n £ \frac|An(q)||GLn(q)| £ c2q-nc_1q^{-n}\leq \frac{|\mathcal{A}_n(q)|}{|\mathrm{GL}_n(q)|}\leq c_2q^{-n} 相似文献
13.
We give a detailed analysis of the proportion of elements in the symmetric group on n points whose order divides m, for n sufficiently large and m≥n with m=O(n).
相似文献
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Let Γ be a graph admitting an arc-transitive subgroup G of automorphisms that leaves invariant a vertex partition with parts of size v≥3. In this paper we study such graphs where: for connected by some edge of Γ, exactly two vertices of B lie on no edge with a vertex of C; and as C runs over all parts of connected to B these vertex pairs (ignoring multiplicities) form a cycle. We prove that this occurs if and only if v=3 or 4, and moreover we give three geometric or group theoretic constructions of infinite families of such graphs. 相似文献
16.
Carmen Amarra Michael Giudici Cheryl E. Praeger 《Designs, Codes and Cryptography》2013,68(1-3):127-139
We study the class of G-symmetric graphs Γ with diameter 2, where G is an affine-type quasiprimitive group on the vertex set of Γ. These graphs arise from normal quotient analysis as basic graphs in the class of symmetric diameter 2 graphs. It is known that ${G \cong V \rtimes G_0}$ , where V is a finite-dimensional vector space over a finite field and G 0 is an irreducible subgroup of GL (V), and Γ is a Cayley graph on V. In particular, we consider the case where ${V = \mathbb {F}_p^d}$ for some prime p and G 0 is maximal in GL (d, p), with G 0 belonging to the Aschbacher classes ${\mathcal {C}_2, \mathcal {C}_4, \mathcal {C}_6, \mathcal {C}_7}$ , and ${\mathcal {C}_8}$ . For ${G_0 \in \mathcal {C}_i, i = 2,4,8}$ , we determine all diameter 2 graphs which arise. For ${G_0 \in \mathcal {C}_6, \mathcal {C}_7}$ we obtain necessary conditions for diameter 2, which restrict the number of unresolved cases to be investigated, and in some special cases determine all diameter 2 graphs. 相似文献
17.
Permutations that have no fixed points have been known for avery long time as derangements. Under that headingRouse-Ball [10, p. 46] puts the matter in the following charmingway: Suppose you have written a letter to each of n differentfriends, and addressed the n corresponding envelopes. In howmany ways can you make the regrettable mistake of putting everyletter into a wrong envelope? He traces this problemback to 1713 and since then it has occurred in one form or anotherin many elementary texts on probability theory (see for example[12, p. 57] and references cited by Rouse-Ball). Let pn be theprobability that all the letters are put into the wrong envelope.It is well known that pne1 as n, and that, moreover,convergence is very fast. In fact, , so that . A derangement can be thought of as a fixed-point-free elementof the symmetric group Sym(n). In this paper we turn our attentionto eigenvalue-free elements of finite linear groups. Since aneigenvector of a linear transformation X in a vector space Vcorresponds to a fixed point of X in the projective space whosepoints are the 1-dimensional subspaces of V, eigenvalue-freeinvertible matrices correspond to derangements in projectivegroups. 相似文献
18.
Silvio Dolfi Robert Guralnick Cheryl E. Praeger Pablo Spiga 《Israel Journal of Mathematics》2016,212(1):107-122
We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that completions of normal local complete intersection domains of finite type over C of dimension ≥ 4 are completions of UFDs of finite type over C. 相似文献
19.
Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication, while at the same time maintaining a constant power output. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family. 相似文献
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