The results we obtain here in the semisimple simply connected case are different than those already known in the case of the adjoint group PGL(2). Finally, we determine the field of definition of such a finite subgroup G of SL(2, (F) over bar), that is, the minimal field F-1 with...
The purpose of this paper is to investigate the influence of subnormal subgroup on finite groups.We obtain some sufficient conditions of solvable finite gr... SU Yue-Bin,KR Wang - 《Journal of Sichuan Normal University》 被引量: 6发表: 2007年 Sylow p-Subgroups and Subnormal Subgroups of Fin...
A subgroup H of a group G is called P-subnormal in G whenever either H=G or there is a chain of subgroups H=H0⊂H1⊂...⊂Hn=G such that |Hi:Hi−1| is a prime for every i=1,2,...,n. We study the structure of a finite group G all of whose Schmidt subgroups are ...
1.19 定义群G的子群H被称为G的正规子群(normal subgroup),如果∀a∈G,b∈H, 有aha−1∈H. 任意阿贝尔群的子群都是正规的,因为aha−1=aa−1h=eh=h.下面给出正规子群的几个等价定义(some alternative characterizations of the property of normality of a subgroup): 1.20 定理 G的子群H是正规的,当...
Let be either a finitely generated free group or a surface group and assume that the isomorphism class of G belongs to . Then, is locally indicable. Proof By Theorem 1.1, G is residually-p , and so it is a subgroup of the completion of G. Since the isomorphism class of G belongs to...
A spectral gap property for subgroups of finite covolume in Lie groups Let G be a real Lie group and H a lattice or, more generally, a closed\nsubgroup of finite covolume in G. We show that the unitary representation\nlambda_{G/H} of G on L^2(G/H) has a spectral gap, that ...
It is known that a core-free permutable subgroup H of a finite group G is always nilpotent [5]; and even when G is not finite, H ... S.,E.,Stonehewer - 《Journal of the Australian Mathematical Society》 被引量: 11发表: 1973年...
nonnormal subgroupcentral extensionWe classify finite p-groups all of whose nonnormal subgroups have orders at most p~3, p odd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3....
to be cyclic,or equivalently,if a ifnite P—group has a self-centralizing cyclic normal subgroup,then the structure of the whole group will be heavily restricted.For example,finite nonabelian P.groups which have a cyclic maximal subgroup(that is clearly a maximal normal Abelian subgroup)were ...
denote the sum of all multiplicities of linear irreducible constituents of \rho . Then we have the following elementary properties: Lemma 2.3 Let H be a subgroup of a finite group G, and let \rho be a complex character of G and \varphi be a complex character of H. Then the following ...