共查询到10条相似文献,搜索用时 125 毫秒
1.
Mong-Lung Lang 《Archiv der Mathematik》1997,68(5):367-370
Let G be a transitive group of degree p+2 with p|G| where p ≧ 5 is a prime number, then (i) G is isomorphic to S
p+2 or A
p+2, if G has an element of order 4, (ii) G is isomorphic to L
2(2
q
) or P Γ L
2 (2
q
), if 2
q
− 1=p is a Mersenne prime and G has no element of order 4. 相似文献
2.
This work examines the existence of (4q
2,2q
2−q,q
2−q) difference sets, for q=p
f
, where p is a prime and f is a positive integer. Suppose that G is a group of order 4q
2 which has a normal subgroup K of order q such that G/K
≅
C
q
×C
2×C
2, where C
q
,C
2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does not admit (4q
2,2q
2−q,q
2−q) difference sets. 相似文献
3.
We call a Cayley digraph Γ = Cay(G, S) normal for G if G
R
, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determine the normality of Cayley digraphs
of valency 2 on nonabelian groups of order 2p
2 (p odd prime). As a result, a family of nonnormal Cayley digraphs is found.
Received February 23, 1998, Revised September 25, 1998, Accepted October 27, 1998 相似文献
4.
LetG denote either of the groupsGL 2 (q) orSL 2 (q). The mapping θ sending a matrix to its transpose-inverse is an automophism ofG and therefore we can form the groupG + =G. <θ>. In this paper conjugacy classes of elements inG + -G are found. These classes are closely related to the congruence classes of invertible matrices inG. 相似文献
5.
Yuriy M. Dyukarev Bernd Fritzsche Bernd Kirstein Conrad Mädler Helge C. Thiele 《Complex Analysis and Operator Theory》2009,3(4):759-834
We study two slightly different versions of the truncated matricial Hamburger moment problem. A central topic is the construction
and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative
Hermitian q × q Borel measures on the real axis which are concentrated on a finite number of points. These points and the corresponding masses
will be explicitly described in terms of the given data. Furthermore, we investigate a particular class of sequences (sj)∞j = 0 of complex q × q matrices for which the corresponding infinite matricial Hamburger moment problem has a unique solution. Our approach is mainly
algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix.
These matrix polynomials are immediate generalizations of the monic orthogonal matrix polynomials associated with a positive
Hermitian block Hankel matrix. We generalize a classical theorem due to Kronecker on infinite Hankel matrices of finite rank
to block Hankel matrices and discuss its consequences for the nonnegative Hermitian case. 相似文献
6.
Martin Cook 《Journal of Algebraic Combinatorics》2010,31(3):319-353
Let G be an adjoint simple algebraic group over an algebraically closed field of characteristic p; let Φ be the root system of G, and take t∈ℕ. Lawther has proven that the dimension of the set G
[t]={g∈G:g
t
=1} depends only on Φ and t. In particular the value is independent of the characteristic p; this was observed for t small and prime by Liebeck. Since G
[t] is clearly a disjoint union of conjugacy classes the question arises as to whether a similar result holds if we replace G
[t] by one of those classes. This paper provides a partial answer to that question. A special case of what we have proven is
the following. Take p,q to be distinct primes and G
p
and G
q
to be adjoint simple algebraic groups with the same root system and over algebraically closed fields of characteristic p and q respectively. If s∈G
p
has order q then there exists an element u∈G
q
such that o(u)=o(s) and
dimuGq=dimsGp\dim u^{G_{q}}=\dim s^{G_{p}}
. 相似文献
7.
As the main result, we show that if G is a finite group such that Γ(G) = Γ(2
F
4(q)), where q = 22m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to 2
F
4(q). We also show that if G is a finite group satisfying |G| =|2
F
4(q)| and Γ(G) = Γ(2
F
4(q)), then G ≅ 2
F
4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2
F
4(q).
The third author was supported in part by a grant from IPM (No. 87200022). 相似文献
8.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D
p
(q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D
p
(q), the subgroup F(G) is equal to 1 for q = 5 and to O
q
(G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
9.
Let G = ℤ
p
, p an odd prime, act freely on a finite-dimensional CW-complex X with mod p cohomology isomorphic to that of a lens space L
2m−1(p; q
1, …, q
m
). In this paper, we determine the mod p cohomology ring of the orbit space X/G, when p
2 ∤ m. 相似文献
10.
Let G be a non-abelian group and associate a non-commuting graph ∇(G) with G as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In this short paper we prove that if G is a finite group with ∇(G) ≅ ∇(M), where M = L
2(q) (q = p
n
, p is a prime), then G ≅ M.
相似文献