共查询到20条相似文献,搜索用时 15 毫秒
1.
Let G be a finite group, and let p1,…, pm be the distinct prime divisors of |G|. Given a sequence 𝒫 =P1,…, Pm, of Sylow pi-subgroups of G, and g ∈ G, denote by m𝒫(g) the number of factorizations g = g1…gm such that gi ∈ Pi. The properly normalized average of m𝒫 over all 𝒫 is a complex character over G whose kernel contains the solvable radical of G [7]. The present paper characterizes the solvable residual of G in terms of this character. 相似文献
2.
特征标次数的重数与可解群结构 总被引:1,自引:1,他引:1
非线性不可约特征标次数的重数全部为1的有限群的分类是熟知的.对可解群,本文讨论更一般的,即非线性不可约特征标次数的重数都与群阶互素的有限群的纯群论性质.特别地,得到了非线性不可约特征标次数的重数均小于2p的奇阶群G的分类结果.这里p为群阶|G|的最小素因子. 相似文献
3.
We study the connection between products of Sylow subgroups of a finite group G and the solvable residual of G. Let Π(𝒫) be a product of Sylow subgroups of G such that each prime divisor of |G| is represented exactly once in Π(𝒫). We prove that there exists a unique normal subgroup N of G which is minimal subject to the requirement Π(𝒫) N = G. Furthermore, N is perfect, and the product of all of these subgroups is the solvable residual of G. We also prove that the solvable residual of G is generated by all elements which arise from non-trivial factorizations of 1 G in such products of Sylow subgroups. 相似文献
4.
Let G be a finite solvable group. The common divisor graph Γ(G) attached to G is a character degree graph. Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor (m, n) > 1. In this article, we classify all graphs with four vertices that may occur as Γ(G) for solvable group G. 相似文献
5.
6.
Guohua Qian 《代数通讯》2013,41(7):2235-2240
The aim of this note is to classify the finite solvable groups with an irreducible character that vanishes on just one class of elements. 相似文献
7.
《代数通讯》2013,41(9):3391-3402
Abstract Let G be a finite, nonabelian, solvable group. Following work by D. Benjamin, we conjecture that some prime must divide at least a third of the irreducible character degrees of G. Benjamin was able to show the conjecture is true if all primes divide at most 3 degrees. We extend this result by showing if primes divide at most 4 degrees, then G has at most 12 degrees. We also present an example showing our result is best possible. 相似文献
8.
9.
Let G be a finite group, p be a prime divisor of |G|, and P be a Sylow p-subgroup of G. We prove that P is normal in a solvable group G if |G : ker φ|p' = φ(1)p' for every nonlinear irreducible monomial p-Brauer character φ of G, where ker φ is the kernel of φ and φ(1)p' is the p'-part of φ(1). 相似文献
10.
The structure of finite solvable groups in which any Sylow subgroup is the product of two cyclic subgroups is studied. In particular, it is proved that the nilpotent length of such a group is no greater than 4. It is also proved that the nilpotent length of a finite solvable group in which the index of any maximal subgroup is either a prime or the square of a prime or the cube of a prime does not exceed 5. 相似文献
11.
Tobias Kildetoft 《代数通讯》2013,41(5):1856-1859
Let cd(G) be the set of degrees of irreducible complex characters and dl(G) be the derived length of the finite group G. It is a result by Gluck that if G is solvable then dl(G) ≤2|cd(G)|. Using a result of Isaacs and Knutson, I will in this article show that this bound can be improved to dl(G) ≤2|cd(G)| ?3 when |cd(G)| ≥3. 相似文献
12.
Péter Pál Pálfy 《Periodica Mathematica Hungarica》1998,36(1):61-65
For any finite solvable group G we show that if three primes dividing the degrees of certain irreducible characters of G are
given, then there exists an irreducible character of G with degree divisible by at least two of the given primes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
Jan-Christoph Schlage-Puchta 《Acta Mathematica Hungarica》2004,105(3):187-195
Define a random variable ξn by choosing a conjugacy class C of the Sylow p-subgroup of Spn by random, and let ξn be the logarithm of the order of an element in C. We show that ξn has bounded variance and mean order log n /log p +O(1), which differs greatly from the average order of elements chosen with equal probability.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
We show that there is no absolute bound on the Fitting height of a group with two Sylow numbers. 相似文献
15.
Cornelia Yuen 《代数通讯》2013,41(12):3909-3911
Jet schemes of monomial schemes are known to be equidimensional but are not reduced in general. We give a formula for the multiplicity along every component of the jet schemes of a simple normal crossing divisor. 相似文献
16.
17.
Simon R. Blackburn 《Discrete Mathematics》2006,306(12):1126-1131
We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings. 相似文献
18.
Alexander Moretó 《Mathematische Nachrichten》2014,287(10):1183-1185
We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ?7, then G is solvable. 相似文献
19.
Michael Wüstner 《Mathematische Nachrichten》1998,192(1):255-267
For a solvable Lie group G the surjectivity of the exponential function expG is equivalent to the connectedness of the near-Cartan subgroups and to the connectedness of the centralizers in a Cartan subgroup of all nilpotent elements in its Lie algebra g. Furthermore, these conditions are satisfied if and only if for all elements g ? G there is an x ? g with g = expG x in which expG is regular. 相似文献
20.
I. D. Ivanyuta 《Acta Appl Math》1998,52(1-3):291-295
In Math. Zh. 36(3) (1963), 240–246, we considered the classification of Sylow p-subgroups of a countable (finitary) symmetric group. Later, we extended this classification to Sylow p-subgroups of a limiting (stable) linear group over a finite field GF(q) with char(GF(q)) p. In this paper, the classification of the Sylow p-subgroups of the limiting (stable) linear group GL() is given for an algebraically closed field of characteristic p. Every Sylow p-subgroup is characterized by a p-adic integer together with a finite or countable cardinal. 相似文献