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1.
In this paper, we study finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels. We prove several results concerning these groups and completely classify 2-groups with at most five nonlinear irreducible characters satisfying this property.  相似文献   

2.
Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P, the subgroup Cl1(ZP) of SK1(ZP), in terms of a genetic basis of P. We also introduce a deflation map Cl1(ZP)Cl1(Z(P/N)), for a normal subgroup N of P, and show that it is always surjective. Along the way, we give a new proof of the result describing the structure of SK1(ZP), when P is an elementary abelian p-group.  相似文献   

3.
2–3 graphs in which each vertex is adjacent to at least two vertices of degree 3 are shown to be characterised by the number of vertices of degree 3 adjacent to vertices of degree 3 only.  相似文献   

4.
Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed between inequivalent harmonic frames and the orbits of a particular set. Secondarily, the symmetry group of prime order harmonic frames is shown to contain a subgroup consisting of a diagonal matrix as well as a permutation matrix, each of which is dependent on the particular harmonic frame in question.  相似文献   

5.
Let S(Gσ)S(Gσ) be the skew adjacency matrix of the oriented graph GσGσ of order n   and λ1,λ2,…,λnλ1,λ2,,λn be all eigenvalues of S(Gσ)S(Gσ). The skew spectral radius ρs(Gσ)ρs(Gσ) of GσGσ is defined as max{|λ1|,|λ2|,…,|λn|}max{|λ1|,|λ2|,,|λn|}. In this paper, we investigate oriented graphs whose skew spectral radii do not exceed 2.  相似文献   

6.
Studied is an assumption on a group that ensures that no matter how the group is embedded in a symmetric group, the corresponding symmetrized tensor space has an orthogonal basis of standard (decomposable) symmetrized tensors.  相似文献   

7.
We consider a parametric nonlinear elliptic inclusion with a multivalued pp-Laplacian-like differential operator and a nonsmooth potential (hemivariational inequality). Using a variational approach based on the nonsmooth critical point theory, we show that for all the values of the parameter in an open half-line, the problem admits at least two nontrivial solutions. Our result extends a recent one by Kristály, Lisei, and Varga [A. Kristály, H. Lisei, C. Varga, Multiple solutions for pp-Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375–1381].  相似文献   

8.
In this note, we show that if is a π-partial character of the π-separable group is a chain of normal subgroups of G, and H is a Hall π-subgroup of G, then has a Fong character α Irr(H) such that for every subgroup , every irreducible constituent of α HN is Fong for N. We also show that if is quasi-primitive, then for every normal subgroup M of G the irreducible constituents of are Fong for M. Received: 21 July 2006 Revised: 17 January 2007  相似文献   

9.
10.
Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials.  相似文献   

11.
We prove a relative version of the theorem of Webb that the augmented chain complex of the p-subgroup complex of a finite group, considered as a complex of modules for the group, is homotopy equivalent to a complex of projectives. This allows us to take into account the group of automorphisms of the group.  相似文献   

12.
Let p>3 be a prime. For each maximal subgroup H?GL(d,p) with |H|?p3d+1, we construct a d-generator finite p-group G with the property that Aut(G) induces H on the Frattini quotient G/Φ(G) and |G|?pd42. A significant feature of this construction is that |G| is very small compared to |H|, shedding new light upon a celebrated result of Bryant and Kovács. The groups G that we exhibit have exponent p, and of all such groups G with the desired action of H on G/Φ(G), the construction yields groups with smallest nilpotency class, and in most cases, the smallest order.  相似文献   

13.
F. Oger proved that if A is a finite group, then the class of groups which are abelian-by-A can be axiomatized by a single first order sentence. It is established here that, in Oger's result, the word abelian cannot be replaced by group. Received: 15 March 1996 / Published online: 18 July 2001  相似文献   

14.
Let n≥23 be an integer and let D2n be the dihedral group of order 2n. It is proved that, if g1,g2,…,g3n is a sequence of 3n elements in D2n, then there exist 2n distinct indices i1,i2,…,i2n such that gi1gi2?gi2n=1. This result is a sharpening of the famous Erd?s-Ginzburg-Ziv theorem for G=D2n.  相似文献   

15.
Let G be a special p-group minimally generated by d3 elements and having derived subgroup of order p12d(d?1). Berkovich asked to find the Schur multiplier and covering groups of such groups G Berkovich and Janko (2011) [1]. We try to give an answer to this question in this article.  相似文献   

16.
The result here answers the following questions in the affirmative: Can the Galois action on all abelian (Galois) fields $K/\mathbb{Q}$ be realized explicitly via an action on characters of some finite group? Are all subfields of a cyclotomic field of the form $\mathbb{Q}(\chi)$, for some irreducible character $\chi$ of a finite group G? In particular, we explicitly determine the Galois action on all irreducible characters of the generalized symmetric groups. We also determine the smallest extension of $\mathbb{Q}$ required to realize (using matrices) a given irreducible representation of a generalized symmetric group. Received: 18 February 2002  相似文献   

17.
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, then we define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix methods. Further, we give the generating function and combinatorial representations of these numbers. Also we present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves.  相似文献   

18.
19.
We give two ways to distinguish from the character table of a finite group G if a Sylow 2-subgroup of G has maximal class. We also characterize finite groups with Sylow 3-subgroups of order 3 in terms of their principal 3-block.  相似文献   

20.
A transitive permutation group of prime degree is doubly transitive or solvable. We give a direct proof of this theorem by Burnside which uses neither S-ring type arguments nor representation theory.Received: 9 December 2004  相似文献   

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