共查询到20条相似文献,搜索用时 15 毫秒
1.
Claude Marion 《代数通讯》2013,41(3):853-925
Let p 1, p 2, p 3 be primes. This is the second article in a series of three on the (p 1, p 2, p 3)-generation of the finite projective special unitary and linear groups PSU3(p n ), PSL3(p n ), where we say a noncyclic group is (p 1, p 2, p 3)-generated if it is a homomorphic image of the triangle group T p 1, p 2, p 3 . This paper is concerned with the case where p 1 = 2 and p 2 = p 3. We determine for any prime p 2 the prime powers p n such that PSU3(p n ) (respectively, PSL3(p n )) is a quotient of T = T 2, p 2, p 2 . We also derive the limit of the probability that a randomly chosen homomorphism in Hom(T, PSU3(p n )) (respectively, Hom(T, PSL3(p n ))) is surjective as p n tends to infinity. 相似文献
2.
Let H be a simple finite classical group not isomorphic to PSL(n, q) for any n, q. We prove that every cyclic subgroup of H has a regular orbit on every nontrivial permutation H-set. 相似文献
3.
Q. Mushtaq 《Southeast Asian Bulletin of Mathematics》2001,25(2):309-312
In this paper we are interested in triangle groups (j, k, l) where j = 2 and k = 3. The groups (j, k, l) can be considered as factor groups of the modular group PSL(2, Z) which has the presentation x, y : x2 = y3 = 1. Since PSL(2,q) is a factor group of Gk,l,m if -1 is a quadratic residue in the finite field Fq, it is therefore worthwhile to look at (j, k, l) groups as subgroups of PSL(2, q) or PGL(2, q). Specifically, we shall find a condition in form of a polynomial for the existence of groups (2, 3, k) as subgroups of PSL(2, q) or PGL(2, q).Mathematics Subject Classification: Primary 20F05 Secondary 20G40. 相似文献
4.
Suppose both A and B are cohopfian groups. Then A × B is cohopfian if A is either extremely noncommutative and torsion free, or finite Abelian, or finite simple. 相似文献
5.
《代数通讯》2013,41(12):4785-4794
Abstract Let ω(G) denote the number of orbits on the finite group G under the action of Aut(G). Using the classification of finite simple groups, we prove that for any positive integer n, there is only a finite number of (non-abelian) finite simple groups G satisfying ω(G) ≤ n. Then we classify all finite simple groups G such that ω(G) ≤ 17. The latter result was obtained by computational means, using the computer algebra system GAP. 相似文献
6.
We show that the symplectic groups PSp6(q) are Hurwitz for all q = p m ≥ 5, with p an odd prime. The result cannot be improved since, for q even and q = 3, it is known that PSp6(q) is not Hurwitz. In particular, n = 6 turns out to be the smallest degree for which a family of classical simple groups of degree n, over 𝔽 p m , contains Hurwitz groups for infinitely many values of m. This fact, for a given (possibly large) p, also follows from [9] and [10]. 相似文献
7.
Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X. 相似文献
8.
Cai Heng Li 《代数通讯》2013,41(11):4722-4743
We determine finite simple groups which have a subgroup of index with exactly two distinct prime divisors. Then from this we derive a classification of primitive permutation groups of degree a product of two prime-powers. 相似文献
9.
Let G be a finite group and let d(G) be the minimal number of generators for G . It is well known that d(G)=2 for all (non-abelian) finite simple groups. We prove that d(H)?4 for any maximal subgroup H of a finite simple group, and that this bound is best possible. 相似文献
10.
We give symmetric presentations for groups closely related to the three sporadic Fischer groups Fi22, Fi23 and Fi24.Mathematics Subject Classiffications (2000). 20D08, 20D06, 20F05This research was supported by an EPSRC grant ref. GR/N27491/01 相似文献
12.
In this paper,it is proved that all the alternating groups A_(p+5) are ODcharacterizable and the symmetric groups S_(p+5) are 3-fold OD-characterizable,where p + 4 is a composite number and p + 6 is a prime and 5≠p∈π(1000!). 相似文献
13.
In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories are ?3 and S3. We also show that the only nonsolvable group with two supercharacter theories is Sp(6,2). 相似文献
14.
Denote by ω(G) the number of orbits of the action of Aut(G) on the finite group G. We prove that if G is a finite nonsolvable group in which ω(G) ≤5, then G is isomorphic to one of the groups A5, A6, PSL(2, 7), or PSL(2, 8). We also consider the case when ω(G) = 6 and show that, if G is a nonsolvable finite group with ω(G) = 6, then either G ≈ PSL(3, 4) or there exists a characteristic elementary abelian 2-subgroup N of G such that G/N ≈ A5. 相似文献
15.
16.
Qunhua Liu 《代数通讯》2013,41(7):2656-2676
We study Schur algebras of classical groups over an algebraically closed field of characteristic different from 2. We prove that Schur algebras are generalized Schur algebras (in Donkin's sense) in types A, C, and D, while this does not hold in type B. Consequently Schur algebras of types A, C, and D are integral quasi-hereditary by Donkin [7, 9]. By using the coalgebra approach we put Schur algebras of a fixed classical group into a certain inverse system. We find that the corresponding hyperalgebra is contained in the inverse limit as a subalgebra. Moreover in types A, C, and D, the surjections in the inverse systems are compatible with the integral quasi-hereditary structure of Schur algebras. 相似文献
17.
We call a subgroup H of a group G nearly s-normal in G if there exists N ? G such that HN ? G and H ∩ N ≤ H sG , where H sG is the largest s-permutable subgroup of G contained in H. In this article, we obtain some results about the nearly s-normal subgroups and use them to characterize the structure of finite groups. 相似文献
18.
In the past thirty years, several kinds of quantitative characterizations of finite groups especially finite simple groups have been investigated by many mathematicians. Such as quantitative characterizations by group order and element orders, by element orders alone, by the set of sizes of conjugacy classes, by dimensions of irreducible characters, by the set of orders of maximal abelian subgroups and so on. Here the authors continue this topic in a new area tending to characterize finite simple groups with given orders by some special conjugacy class sizes, such as largest conjugacy class sizes, smallest conjugacy class sizes greater than 1 and so on. 相似文献
19.
Martin Hildebrand 《Journal of Theoretical Probability》2001,14(4):1019-1034
This paper considers lazy random walks supported on a random subset of k elements of a finite group G with order n. If k=a log2
n where a>1 is constant, then most such walks take no more than a multiple of log2
n steps to get close to uniformly distributed on G. If k=log2
n+f(n) where f(n) and f(n)/log2
n0 as n, then most such walks take no more than a multiple of (log2
n) ln(log2
n) steps to get close to uniformly distributed. To get these results, this paper extends techniques of Erdös and Rényi and of Pak. 相似文献
20.
Let S be a Sylow 2-subgroup of a finite simple group and let S=S1×S2××Sk be the direct product and each component Si, i=1,2,...,k is indecomposable. In this article, we prove that each Si is also a Sylow 2-subgroup of some simple group.
Mathematics Subject Classifications (2000) 20E32, 20D20. 相似文献