有关Clifford矩阵群的几个离散性判别准则

研究了Clifford矩阵变换群的离散性质,给出了几个判别离散群的不等式和定理.     

Finite groups with systems of Σ-embedded subgroups

In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = ...     

Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement

In this note,we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable.This gives a positive answer to Problem 17.111 of the Kourovka Notebook(Unsolved Problems in Group Theory),which was posed by Skiba.     

由双边群相关Hopf模诱导的Morita等价

Let H be a Hopf π-coalgebra over a commutative ring k with bijective antipode S, and A and B right π-H-comodulelike algebras. We show that the pair of adjoint functors （F3 = A  Bop A□ HBop -,G3 = （-）coH） between the categories A□HBopM and AMπB-H is a pair of inverse equivalences, when A is a faithfully flat π-H-Galois extension. Furthermore, the categories Moritaπ-H（A,B） and Morita □π-H（AcoH,BcoH） are equivalent, if A and B are faithfully flat π-H-Galois extensions.     

On the Structure of the Augmentation Quotient Group for Some Non-abelian p-groups

In this paper,we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p,where p is an odd prime,and k is greater than or equal to 3.A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.     

Integral Cayley Graphs over Finite Groups

We prove that the spectrum of a Cayley graph over a finite group with a normal generating set S containing with every its element s all generators of the cyclic group(s)is integral.In particular,a Cayley graph of a 2-group generated by a normal set of involutions is integral.We prove that a Cayley graph over the symmetric group of degree n no less than 2 generated by all transpositions is integral.We find the spectrum of a Cayley graph over the alternating group of degree n no less than 4 with a generating set of 3-cycles of the form(k i j)with fixed k,a s{-n+1,1-n+1,2^2-n+1,...,(n-1)2-n+1}.     

On the Group of p-endotrivial kG-modules

In this paper,we define a group Tp(G) of p-endotrivial kG-modules and a generalized Dade group Dp(G) for a finite group G.We prove that Tp(G) ≌ Tp(H) whenever the subgroup H contains a normalizer of a Sylow p-subgroup of G,in this case,K(G) ≌ K(H).We also prove that the group Dp(G) can be embedded into Tp(G) as a subgroup.     

Two Notes on Top ological Groups

In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.     

A note on Rubin''''s methods of the use of two Euler systems

Here we show that Rubin’s method of the use of two Euler systems to the proofs of Iwasawa main conjectures of the rational number field and of an imaginary quadratic field is only proper to these two kinds of number fields. We mainly use the properties of adéle ring and idéle group in class field theory to get the result.     

On representations of real Jacobi groups

We consider a category of continuous Hilbert space representations and a category of smooth Fr’echet representations,of a real Jacobi group G.By Mackey’s theory,they are respectively equivalent to certain categories of representations of a real reductive group L.Within these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each other.By using Casselman-Wallach’s theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of G.We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.