共查询到20条相似文献,搜索用时 15 毫秒
1.
Emanuele Pacifici 《Archiv der Mathematik》2005,84(1):1-10
Let G be a finite group, and V a finite-dimensional semisimple G-module over a finite field. Assume that V is endowed with a nonsingular bilinear form which is symmetric or symplectic, and which is invariant under the action of G. In this setting, we compute the number of anisotropic simple submodules of V.Received: 25 May 2004 相似文献
2.
If π is a set of primes, a finite group G is block π-separated if for every two distinct irreducible complex characters α, β ∈ Irr(G) there exists a prime p ∈ π such that α and β lie in different Brauer p-blocks. A group G is block separated if it is separated by the set of prime divisors of |G|. Given a set π with n different primes, we construct an example of a solvable π-group G which is block separated but it is not separated by every proper subset of π.
Received: 22 December 2004 相似文献
3.
Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the
intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|.
Received: 26 January 2005 相似文献
5.
Rasheed M. S. Mahmood 《Mediterranean Journal of Mathematics》2009,6(1):87-103
In this paper we show that if G is a group acting on a graph X with inversions such that G has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.
Received: January 3, 2007., Revised: August 10, 2007 and May 3, 2008., Accepted: October 17, 2008. 相似文献
6.
Fabrice Krieger 《Geometriae Dedicata》2006,122(1):15-31
Let G be an infinite countable residually finite amenable group. In this paper we construct a continuous action of G on a compact metrisable space X such that the dynamical system (X, G) cannot be embedded in the G-shift on [0,1]
G
. This result generalizes a construction due to E. Lindenstrauss and B. Weiss (Mean topological dimension, Israel J. Math. 115 (2000), 1–24) for
. 相似文献
7.
A subgroup H of G is said to be $\pi$-quasinormal in G if it
permute with every Sylow subgroup of G.
In this paper, we extend the study on the structure of a finite group under the
assumption that some subgroups of G are
$\pi$-quasinormal in G. The main result we proved
in this paper is the following:Theorem 3.4.
Let ${\cal F}$ be a saturated formation
containing the supersolvable groups. Suppose that G is a group with a
normal subgroup H such that $G/H \in {\cal F}$,
and all maximal subgroups of any Sylow subgroup of $F^{*}(H)$ are $\pi$-quasinormal in
G, then $G \in {\cal F}$.
Received: 10 May 2002 相似文献
8.
Atournament regular representation (TRR) of an abstract groupG is a tournamentT whose automorphism group is isomorphic toG and is a regular permutation group on the vertices ofT. L. Babai and W. Imrich have shown that every finite group of odd order exceptZ
3 ×Z
3 admits a TRR. In the present paper we give several sufficient conditions for an infinite groupG with no element of order 2 to admit a TRR. Among these are the following: (1)G is a cyclic extension byZ of a finitely generated group; (2)G is a cyclic extension byZ
2n+1 of any group admitting a TRR; (3)G is a finitely generated abelian group; (4)G is a countably generated abelian group whose torsion subgroup is finite. 相似文献
9.
In a finite group G every element can be factorized in such a way that there is one factor for each prime divisor p of | G |, and the order of this factor is pα for some integer α ≧ 0. We define g ∈G to be uniquely factorizable if it has just one such factorization (whose factors must be pairwise commuting). We consider the existence of uniquely factorizable
elements and its relation to the solvability of the group. We prove that G is solvable if and only if the set of all uniquely factorizable elements of G is the Fitting subgroup of G. We also prove various sufficient conditions for the non-existence of uniquely factorizable elements in non-solvable groups.
Received: 9 June 2005 相似文献
10.
In [1, 3] it was shown: Theorem A. If G is the fundamental group of a finite graph of λ-dimensional duality groups with |G
o(e) : G
e
| < ∞ and |G
τ(e) : G
e
| < ∞ for every edge e of the corresponding G-tree, then G is an (λ + 1)-dimensional duality group.
Here we use the methods of Brown and Geoghegan in [3] to obtain examples of duality groups under weaker conditions than those
of Theorem A.
Received: 5 June 2007 相似文献
11.
Luis Paris 《Mathematische Annalen》2002,322(2):301-315
Let G be a countable discrete group. Call two subgroups and of G commensurable if has finite index in both and . We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the map
ping class group on the complex of curves has noncommensurable stabilizers. Following a method due to Burger and de la Harpe,
this action leads to constructions of irreducible unitary representations of the mapping class group.
Received: 26 July 1999 / Revised version: 14 May 2001 / Published online: 19 October 2001 相似文献
12.
We prove conditions for a product of distinct subgroups of an arbitrary group G to be a subgroup of G. In particular, the normal closure of any A ≤ G is equal to the product of some distinct conjugates of A. As an application of the later result we derive constraints on the size of a nontrivial conjugacy class of a finite non-Abelian simple group. 相似文献
13.
A. Laradji 《Archiv der Mathematik》2002,79(6):418-422
Let π be a set of prime numbers andG a finite π-separable group. Let θ be an irreducible π′-partial character of a normal subgroupN ofG and denote by Iπ′ (G‖θ), the set of all irreducible π′-partial characters Φ ofG such that θ is a constituent of ΦN. In this paper, we obtain some information about the vertices of the elements in Iπ′ (G‖θ). As a consequence, we establish an analogue of Fong's theorem on defect groups of covering blocks, for the vertices of
the simple modules (in characteristicsp) of a finitep-solvable group lying over a fixed simple module of a normal subgroup. 相似文献
14.
15.
16.
We prove that a block of a finite strongly p-solvable group G with defect group P is Morita equivalent to its corresponding block of NG(Z(J (P))) via a bimodule with endopermutation source.
Received: 7 December 2005 相似文献
17.
Martin Lorenz 《Commentarii Mathematici Helvetici》1994,69(1):474-482
LetG be a finite group acting by automorphisms on an algebraS over some commutative ringk. We show that if the action ofG restricted to the center ofS is Galois in the sense of [C-H-R], thenHH
*(S
G)≊HH
*
(S)
G. An analogous result holds for cyclic homology, provided the order ofG is invertible ink.
The author was supported in part by a grant from the NSF. 相似文献
18.
In this paper we shall deal with a weak version of the Borsuk-Ulam theorem for
G-isovariant maps, which we call the weak isovariant Borsuk-Ulam theorem.
One of the results is that the weak isovariant Borsuk-Ulam theorem in linear
G-spheres holds for an arbitrary compact
Lie group G. On the contrary the weak isovariant
Borsuk-Ulam theorem in semilinear G-(homology)
spheres holds if and only if G is solvable.
Received: 2 April 2002 相似文献
19.
A subgroup H of a finite group
G is called c-normal in
G if there exists a normal subgroup
N of G such that
G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups
of which every maximal subgroup of its Sylow
p-subgroup is c-normal and the
class of groups of which some minimal subgroups of its Sylow
p-subgroup is c-normal for some prime number
p. Some interesting results are obtained and
consequently, many known results related to
p-nilpotent groups and
p-supersolvable groups are generalized. 相似文献
20.
《Mathematische Nachrichten》2018,291(8-9):1390-1399