共查询到20条相似文献,搜索用时 0 毫秒
1.
Houshang Behravesh 《Southeast Asian Bulletin of Mathematics》2000,24(3):345-353
By a quasi-permutation matrix we mean a square matrix over the complex field with non-negative integral trace. Thus every permutation matrix over is a quasi-permutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q (G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field , and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. In this paper we will calculate c(G), q(G), and p(G), where G is a metacyclic p-group with non-cyclic center and p is either 2 or an odd prime number.AMS Subject Classification (2000) 20C15 相似文献
2.
In this work we analyze p-groups of class 2 G and H, with same rational group algebras. We prove that if QG = QH, then their commutators are equal and the centers, 𝒵(G) and 𝒵(H), have their orders preserved. We apply our results to Frattini Central p-groups, and we present an example of two groups of order p 7, with no isomorphic centers and different central cyclic components intersecting the cyclic components of the respective commutators groups. 相似文献
3.
《数学学报(英文版)》2017,(5)
A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group,the normalizer N_G(P) controls p-fusion in G. Let P be a central extension as 1→ Z_(p~m)→ P→ Z_p ×···× Z_p→1,and |P'|≤p,m≥2. The purpose of this paper is to prove that P is resistant. 相似文献
4.
5.
《数学学报(英文版)》2017,(2)
Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in Φ(G) have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified. 相似文献
6.
M. Shabani-Attar 《代数通讯》2013,41(6):2437-2442
Let G be a finite non-abelian p-group, where p is a prime. An automorphism α of G is called a class preserving automorphism if α(x) ∈ x G the conjugacy class of x in G, for all x ∈ G. An automorphism α of G is called an IA-automorphism if x ?1α(x) ∈ G′ for each x ∈ G. In this paper, we give necessary and sufficient conditions on finite p-group G of nilpotency class 2 such that every IA-automorphism is class preserving. 相似文献
7.
Manoj K. Yadav 《代数通讯》2013,41(12):4576-4592
We obtain certain results on a finite p-group whose central automorphisms are all class preserving. In particular, we prove that if G is a finite p-group whose central automorphisms are all class preserving, then d(G) is even, where d(G) denotes the number of elements in any minimal generating set for G. As an application of these results, we obtain some results regarding finite p-groups whose automorphisms are all class preserving. 相似文献
8.
9.
Eduard Looijenga 《Geometriae Dedicata》1997,64(1):69-83
Let S be a closed orientable surface of genus at least 2 and let
to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H1(
). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group. 相似文献
10.
确定了一类中心循环的有限p-群G的自同构群.设G=X_3(p~m)~(*n)*Z_(p~(m+r)),其中m≥1,n≥1和r≥0,并且X_3(p~m)=x,y|x~(p~m)=y~(p~m)=1,[x,y]~(p~m)=1,[x,[x,y]]=[y,[x,y]]=1.Aut_nG表示Aut G中平凡地作用在N上的元素形成的正规子群,其中G'≤N≤ζG,|N|=p~(m+s),0≤s≤r,则(i)如果p是一个奇素数,那么AutG/Aut_nG≌Z_(p~((m+s-1)(p-1))),Aut_nG/InnG≌Sp(2n,Z_(p~m))×Z_(p~(r-s)).(ii)如果p=2,那么AutG/Aut_nG≌H,其中H=1(当m+s=1时)或者Z_(2~(m+s-2))×Z_2(当m+s≥2时).进一步地,Aut_nG/InnG≌K×L,其中K=Sp(2n,Z_(2~m))(当r0时)或者O(2n,Z_(2~m))(当r=0时),L=Z_(2~(r-1))×Z_2(当m=1,s=0,r≥1时)或者Z_(2~(r-s)). 相似文献
11.
Paolo Boggiatto Carmen Fern��ndez Antonio Galbis 《Journal of Fourier Analysis and Applications》2011,17(6):1180-1197
In this paper we consider a version of the uncertainty principle concerning limitations on the supports of time-frequency representations in the Cohen class. In particular we obtain various classes of kernels with the property that the corresponding representations of non trivial signals cannot be compactly supported. As an application of our results we show that a linear partial differential operator applied to the Wigner distribution of a function f≠0 in the Schwartz class cannot produce a compactly supported function. 相似文献
12.
13.
14.
15.
16.
17.
Let S be a subgroup of a group G. A set ${\Pi= \{H_1, \ldots , H_n\}}$ of subgroups ${H_i (i = 1, \ldots ,n)}$ with ${G=\cup_{H_i\in\Pi}H_i}$ is said to be an equal quasi-partition of G if ${H_i\cap H_j\cong S}$ and ${|H_i|=|H_j|}$ for all ${H_i, H_j\in\Pi}$ with ${i\ne j}$ . In this paper we investigate finite p-groups such that a subset of their maximal subgroups form an equal quasi-partition. 相似文献
18.
E. I. Khukhro 《Algebra and Logic》2000,39(3):207-214
We consider the action of a p-group G on an Abelian p-group A, with the latter treated as a faithful right ℤG-module. Our
aim is to establish a connection between exponents of the kernels under the induced action of G on elementary p-groups A/pA
and Ω1(A) = {x ε A|px=0}; the kernels are denoted by CG(A/pA) and CG(Ω1(A)), respectively. It is proved that if the exponent of one of the kernels CG(A/pA) or CG(Ω1(A)) is finite then the other also has a finite exponent bounded in terms of the first; moreover, these kernels are nilpotent.
In one case we impose the additional restriction
. And the wreath product
of a quasicyclic group and an arbitrary p-group G shows that this condition cannot be dropped. The results obtained are used
to confirm, for one particular case, the conjecture on the boundedness of a derived length of a finite group with an automorphism
of order 2 all of whose fixed points are central. (The solubility of such groups, and also the reduction to the case of 2-groups,
were established in [1].)
Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 359–371, May–June, 2000. 相似文献
19.
20.
Coy L. May 《代数通讯》2013,41(10):4402-4413
Let G be a finite group. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts. We show that a non-cyclic p-group G has symmetric genus not congruent to 1(mod p 3) if and only if G is in one of 10 families of groups. The genus formula for each of these 10 families of groups is determined. A consequence of this classification is that almost all positive integers that are the genus of a p-group are congruent to 1(mod p 3). Finally, the integers that occur as the symmetric genus of a p-group with Frattini-class 2 have density zero in the positive integers. 相似文献