FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

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On Discrete Zariski-Dense Subgroups of Algebraic Groups

We investigate under which conditions an algebraic group G defined over a locally compact field k admitr a subgroup Γ? G(k) which is dense in the Zariski topology, but discerte in the topology induced by the locally compact topology on k. For non—solvable groups we provide a complete answer.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.     

某些子群介于正规与反正规之间的有限群北大核心CSCD

有限群G的子群H称为G的BNA子群,若对任意的x∈G有H^(x)=H或x∈.若有限群G的所有素数阶和4阶循环子群都是G的BNA子群,则称G为CBNA群.本文主要刻画CBNA群的结构,并且给出所有真子群都是CBNA群的完全分类.     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

Recognition of subgroups of direct products of hyperbolic groups

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic.

     

On the normality of the rings of Schubert varieties

We prove that the cone over a Schubert variety inG/P (P being a maximal parabolic subgroup of classical type) is normal by exhibiting a 2-regular sequence inR(w) (the homogeneous coordinate ring of the Schubert varietyX(w) inG/P under the canonical protective embeddingG/P ⊂→ (p (H° G/P,L)),L being the ample generator of (PicG/P), which vanishes on the singular locus ofX(w). We also prove the surjectivity ofH° (G/Q, L) H° (X(w), L), whereQ is a classical parabolic subgroup (not necessarily maximal) ofG andL is an ample line bundle onG/Q.     

P2-阶子群X-ss-半置换的有限群

设G是有限群,X是G的一个非空子集,子群H称为在G中X-ss-半置换,若H在G中有补充子群T,对于T的任意Sylowp-子群P,只要(p,|H|)=1,就存在x∈X使得HP^x=P^xH。通过对p²-阶子群的X-ss-半置换性研究,得到了p-幂零群的新判断。     

ON A CHAIN OF BUTLER GROUPS

1IntroductionThenotationandtelliluologyusedwillmainlyconformtothatof[5].Werecall11ereafewfundamentalnotions.Inthispaper,groupmeansabeliangroup,qdenotestheadditivegroupOfrationals,ZdenotesthegroupOfintegers.Atypeisanequivalenceclassofheightsequences.IfSisafinitesetoftypestheniuf(S)andsup(S)aretypes,whereinf(S)andsup(S)aregivenbycomponentndninlumsandmaximumsofheightsequencesrepresentingtypesinS.Twotorsionfi'eegroupsAandBarequasi-isolllorphicifthereisfEHorn(A,B)suchthatIisamonomorphismand…