共查询到20条相似文献,搜索用时 0 毫秒
1.
A digraph \({\overrightarrow{\mathcal{Pc}}(G)}\) is said to be the directed power graph on the conjugacy classes of a group G, if its vertices are the non-trivial conjugacy classes of G, and there is an arc from vertex C to C′ if and only if \({C \neq C'}\) and \({C \subseteqq {C'}^{m}}\) for some positive integer \({m > 0}\). Moreover, the simple graph \({\mathcal{Pc}(G)}\) is said to be the (undirected) power graph on the conjugacy classes of a group G if its vertices are the conjugacy classes of G and two distinct vertices C and C′ are adjacent in \({\mathcal{Pc}(G)}\) if one is a subset of a power of the other. In this paper, we find some connections between algebraic properties of some groups and properties of the associated graph. 相似文献
2.
Let $G$ be a finite group and $\mathrm{bcl}(G)$ the largest conjugacy class length of $G$ . In this note we slightly improve He and Shi’s lower bound for $\mathrm{bcl}(G)$ , showing that $|\mathrm{bcl}(G)|\ge p^{\frac{1}{p}}(|G:O_{p}(G)|_{p})^{\frac{p-1}{p}}$ . 相似文献
5.
A finite group with a normal subgroup containing almost all conjugacy classes except one, two, or three ones is considered. Sufficient monomiality conditions for such group are found for each of these cases. It turns out that additional conditions are not required in the first case. 相似文献
6.
In this work we obtain new properties connected with the number of conjugacy classes of elements of a finite group, through
the analysis of the number r
G(gN) of conjugacy classes of elements of G that intersect the coset gN, where N is a normal subgroup of G and g any element of G. The results obtained about this number are not only used in the general problem of classifying finite groups according to
the number of conjugacy classes, but they also allow us to improve and generalize known results relating to conjugacy classes
due to P. Hall, M. Cartwright, A. Mann, G. Sherman, A. Vera-López and L. Ortíz de Elguea. Examples are given which illustrate
our improvements.
This work has been supported by the University of the Basque Country. 相似文献
8.
Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK?1 = 1 ∪ D ∪ D?1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions on the class sizes determining the solvability and the structure of 〈 K〉 and 〈 D〉. 相似文献
9.
We present some arithmetical-type conditions on the set of conjugacy classes of a finite group that are sufficient for the
monomiality of the group, i.e., for the property that all its irreducible complex characters are induced by linear characters
of subgroups.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 5, pp. 201–212, 2007. 相似文献
10.
The distribution of primitive conjugacy classes of the fundamental group of graphs in the first homology group of the graphs
is studied in some special cases. Bibliography: 10 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 154–165.
Translated by A. M. Nikitin. 相似文献
11.
We show that for many formations \frak F\frak F, there exists an integer n = [`( m)](\frak F)n = \overline m(\frak F) such that every finite soluble group G not belonging to the class \frak F\frak F has at most n conjugacy classes of maximal subgroups belonging to the class \frak F\frak F. If \frak F\frak F is a local formation with formation function f, we bound [`( m)](\frak F)\overline m(\frak F) in terms of the [`( m)]( f( p))( p ? \Bbb P )\overline m(f(p))(p \in \Bbb P ). In particular, we show that [`( m)](\frak Nk) = k+1\overline m(\frak N^k) = k+1 for every nonnegative integer k, where \frak Nk\frak N^k is the class of all finite groups of Fitting length £ k\le k. 相似文献
12.
Let m, n > 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1 ,m, n,mn}. 相似文献
13.
We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1( G, Pic( X)) for cyclic groups of prime order. 相似文献
14.
We prove that a holomorphic vector bundle over a compact connected Kähler manifold admits a flat connection, with a finite group as its monodromy, if and only if there are two distinct polynomials and , with nonnegative integral coefficients, such that the vector bundle is isomorphic to . An analogous result is proved for vector bundles over connected smooth quasi-projective varieties, of arbitrary dimension, admitting a flat connection with finite monodromy group. When the base space is a connected projective variety, or a connected smooth quasi-projective curve, the above characterization of vector bundles admitting a flat connection with finite monodromy group was established by M. V. Nori. 相似文献
17.
Let G be a finite group and let x G denote the conjugacy class of an element x of G. We classify all finite groups G in the following three cases: (i) Each non-trivial conjugacy class of G together with the identity element 1 is a subgroup of G, (ii) union of any two distinct non-trivial conjugacy classes of G together with 1 is a subgroup of G, and (iii) union of any three distinct non-trivial conjugacy classes of G together with 1 is a subgroup of G. 相似文献
18.
We presentmethods for verification of the following conjecture: A nonidentity conjugacy class in a finite simple group contains two commuting elements. By way of illustration, we consider sporadic groups, the projective group Ln( q) and the alternating group An. 相似文献
19.
Let G be a finite group. The question of how certain arithmetical conditions on the lengths of the conjugacy classes of G influence the group structure has been studied by several authors. In this paper we study restrictions on the structure of a finite group in which the lengths of conjugacy classes are not divisible by p 2 for some prime p. We generalise and provide simplified proofs for some earlier results. 相似文献
20.
The purpose of this paper is to investigate influences of lengths of conjugacy classes of finite groups on the structure of finite groups. We get a necessary and sufficient condition for a finite group
G to be equal to
Op( G)× Op′( G). We also generalize some results (Comm. Algebra 27 (9) (1999) 4347). 相似文献
|