Search results for "combinatoric"

Fixed point spaces, primitive character degrees and conjugacy class sizes

2006

Let G be a finite group that acts on a nonzero finite dimensional vector space V over an arbitrary field. Assume that V is completely reducible as a G-module, and that G fixes no nonzero vector of V. We show that some element g ∈ G has a small fixed-point space in V. Specifically, we prove that we can choose g so that dim C V (g) < (1/p)dim V, where p is the smallest prime divisor of |G|.

Irreducibility of Hurwitz spaces of coverings with one special fiber

2006

Abstract Let Y be a smooth, projective complex curve of genus g ⩾ 1. Let d be an integer ⩾ 3, let e = {e1, e2,..., er} be a partition of d and let | e | = Σi=1r(ei − 1). In this paper we study the Hurwitz spaces which parametrize coverings of degree d of Y branched in n points of which n − 1 are points of simple ramification and one is a special point whose local monodromy has cyclic type e and furthermore the coverings have full monodromy group Sd. We prove the irreducibility of these Hurwitz spaces when n − 1 + | e | ⩾ 2d, thus generalizing a result of Graber, Harris and Starr [A note on Hurwitz schemes of covers of a positive genus curve, Preprint, math. AG/0205056].

Polynomial identities with involution and the hyperoctahedral group

1987

On the abnormal structure of finite groups

2014

We study finite groups in which every maximal subgroup is supersoluble or normal. Our results answer some questions arising from papers of Asaad and Rose.

Products of groups and group classes

1994

Letχ be a Schunck class, and let the finite groupG=AB=BC=AC be the product of two nilpotent subgroupsA andB andχ-subgroupC. If for every common prime divisorp of the orders ofA andB the cyclic group of orderp is anχ-group, thenG is anχ-group. This generalizes earlier results of O. Kegel and F. Peterson. Some related results for groups of the formG=AB=AK=BK, whereK is a nilpotent normal subgroup ofG andA andB areχ-groups for some saturated formationχ, are also proved.

On generalised subnormal subgroups of finite groups

2013

Let be a formation of finite groups. A subgroup M of a finite group G is said to be -normal in G if belongs to . A subgroup U of a finite group G is called a K--subnormal subgroup of G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ … ≤ Un = G such that Ui − 1 is either normal or -normal in Ui, for i = 1, 2, …, n. The K--subnormality could be regarded as the natural extension of the subnormality to formation theory and plays an important role in the structural study of finite groups. The main purpose of this paper is to analyse classes of finite groups whose K--subnormal subgroups are exactly the subnormal ones. Some interesting extensions of well-known classes of groups emerge.

On Hurwitz spaces of coverings with one special fiber

2009

Let X X' Y be a covering of smooth, projective complex curves such that p is a degree 2 etale covering and f is a degree d covering, with monodromy group Sd, branched in n + 1 points one of which is a special point whose local monodromy has cycle type given by the partition e = (e1,...,er) of d. We study such coverings whose monodromy group is either W(Bd) or wN(W(Bd))(G1)w-1 for some w in W(Bd), where W(Bd) is the Weyl group of type Bd, G1 is the subgroup of W(Bd) generated by reflections with respect to the long roots ei - ej and N(W(Bd))(G1) is the normalizer of G1. We prove that in both cases the corresponding Hurwitz spaces are not connected and hence are not irreducible. In fact, we s…

On mutually permutable products of finite groups

2005

Abstract In this paper a structural theorem about mutually permutable products of finite groups is obtained. This result is used to derive some results on mutually permutable products of groups whose chief factors are simple. Some earlier results on mutually permutable products of supersoluble groups appear as particular cases.

Tsen–Lang Theory for Cpi-fields

1995

On totally permutable products of finite groups

2005

[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, PT, and PST-groups.