A Lower Bound on Unknotting Number

In this paper the authors use a modified Wirtinger presentation to give a lower bound on the unknotting number of a knot in S3.     

子群为共轭置换或自正规的群

对所有子群皆为共轭置换或自正规的有限群进行了研究,获得了这类群的一些性质,并进行了分类.     

区间值直觉模糊超子群

在K.Atanassov引进区间值直觉模糊集的基础上,给出了区间值直觉模糊超子群的定义,刻画了其特征结构,研究了这类区间值直觉模糊超群的同态像及原像等问题.同时,讨论了区间值直觉模糊超子群与区间值直觉模糊子群的关系.     

有限群的s-条件置换子群

如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HT~x=T~xH,那么称群G的子群H在G中s-条件置换．利用s-条件置换子群给出了一些群的性质和结构．     

A generalization of Gram–Schmidt orthogonalization generating all Parseval frames

Given an arbitrary finite sequence of vectors in a finite-dimensional Hilbert space, we describe an algorithm, which computes a Parseval frame for the subspace generated by the input vectors while preserving redundancy exactly. We further investigate several of its properties. Finally, we apply the algorithm to several numerical examples.      

S-半正规性与P-幂零性

In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of main results, some sufficient conditions for finite nilpotent groups and finite supersolvable groups are obtained.     

A characterization of finite simple groups by the orders of solvable subgroups

Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn(q), where n≥3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori.     

Finite groups with 2-nilpotent subgroups of even index

Finite groups with 2-nilpotent subgroups of even index are described. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 700–705, May, 1997. Translated by A. I. Shtern     

The <Emphasis Type="Italic">F</Emphasis>-local subgroups of the groups with a generalized finite element of order 2 or 4

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of infinite locally finite subgroups in the groups with almost finite almost solvable elements of order 2 and 4 and in the groups with almost finite elements.     

Finite groups with a seminormal Hall subgroup

Tests for π-solvability of a finite group with seminormal Hall π-subgroup are established and the nilpotency of the third commutator subgroup of any group with seminormal noncyclic Sylow subgroups is proved.