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.

FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP

For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.

Finite p-groups with abelian maximal subgroups generated by two elements

Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an M_(n)-group.For p=2,M_(2)-groups have been classified.For odd prime p,this paper provides the isomorphism classification of M_(2)-groups,thereby achieving a complete classification of M_(2)-groups.

On Non-commuting Sets in a Finite p-group with Derived Subgroup of Prime Order

Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.

Finite p-Groups G with H'=G'for Each A2-Subgroup H^(*)

A finite p-group G is called an At-group if t is the minimal non-negative integer such that all subgroups of index pt of G are abelian.The finite p-groups G with H'=G'for all A2-subgroups H of G are classified completely in this paper.As an application,a problem proposed by Berkovich is solved.

环Fp^k+uFp^k上的一类常循环码

常循环码是一类重要的纠错码,文章讨论了环Fpk+uFpk上长为n的(1+αu)-循环码、(ξi+αu)-循环码的置换等价性,并得出2种循环码的Gray像均置换等价于Fpk上长为pkn、指数为pk-1的准循环码。

无限正则p-群

对一类无限正则p-进行了研究,得到了一个正则的局部幂零P-群G如果满足|G:(?)_1(G)|<∞,那么G是幂零的且G是可除阿贝尔P-群被有限群的扩张.进而,还研究了一类无限的非正则p-群,但它的所有真商群或者真的无限子群是正则群.在假设这类群存在拟循环子群的情况下,在定理1.2和1.3给出了这类群的结构的刻画.

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解Cernikov p-群的结构.

基于PEG-QC算法的LDPC码校验矩阵的构造

通过分析LDPC(Low Density Parity Check)码树图、PEG(Progressive Edge-Growth)算法和准循环LDPC码的特点,提出了一种将PEG算法和准循环矩阵相结合来构造LDPC码校验矩阵的新算法.在该算法中,首先利用PEG算法构造基矩阵,再用文中提出的移位参数公式和准循环LDPC码结构特点来构造循环置换矩阵;然后利用循环置换矩阵和全零矩阵对基矩阵进行扩展,从而得到围长至少为8的准循环LDPC码校验矩阵.该算法综合了PEG算法和准循环码的优点,纠错性能总体上好于PEG算法,在相同的码参数条件下的硬件实现比PEG算法简单,且参数选择具有较大灵活性.

所有无限真子群是阿贝尔群的局部幂零p-群

主要研究每一个无限真子群都是阿贝尔群的局部幂零p-群.给出了这类群的结构的详细刻画,得到了:定理1设群G是局部幂零p-群,若G不是阿贝尔群,但是G中的每一个无限真子群是阿贝尔群,则(1)当G不是幂零群时,G是秩为p-1的可除阿贝尔p-群被循环群的扩张;(2)当G是幂零群时,G是极小非阿贝尔p-群与拟循环p-群的乘积.

p阶拟循环群理论的超稳定性

依次用Δ- 秩、U -秩与SU- 秩证明了p阶拟循环群理论的稳定性、超稳定性与超单纯性,并计算了该理论中一元与二元完全型的CB -秩,证明了该理论中任意n元型的CB -秩均小于ω1.

p阶拟循环群理论的可数模型

讨论了p阶拟循环群理论的可数的饱和模型,并用强极小理论证明了p阶拟循环群理论是ω1 范畴的,进而 p阶拟循环群理论的每一模型都是齐次模型.

码率为2／3的大数逻辑可译二进制突发错误纠错码

采用构造码率为１／２的大数逻辑可译二进制突发错误纠错码的方法，提出了构造码率为２／３的（３ｍ，２ｍ）大数逻辑可译二进制突发错误纠错码，该码能够纠正所有长度小于等于ｂ（６＝［３（ｍ－１＋ｈ）／（１２＋ｈ）］，其中ｈ＝［（ｍ－１）１２／１２］）的闭环突发错误模式。

只含一个p阶子群的无限p-群

若群G有上升列1=G_0<G_1<…<G_β=G β为某一序数其中任意相邻二群G_i<G_(i+1) 恒有Abel子群A_i存在,使G_iA_i=G_(i+1),则称G为AI-群.证明了:设无限p-群P仅含一个p阶子群.若p=2,则P同构于Z(2~∞)或局部广四元数群:a^2=b_1 b_1~2=1 b_(n+1)~2=b_n b_n^n=b_n^(-1) n=1,2…若p为奇素数,且P为局部AI-群,则P同构于Z(p~∞).

Finite p-Groups all of Whose Subgroups of Index p^(3) are Abelian

Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian group.From the definition,we know every finite non-abelian p-group can be regarded as an A_(t)-group for some positive integer t.A_(1)-groups and A_(2)-groups have been classified.Classifying A_(3)-groups is an old problem.In this paper,some general properties about A_(t)-groups are given.A_(3)-groups are completely classified up to isomorphism.Moreover,we determine the Frattini subgroup,the derived subgroup and the center of every A_(3)-group,and give the number of A_(1)-subgroups and the triple(μ_(0),μ_(1),μ_(2))of every A_(3)-group,whereμi denotes the number of A_(i)-subgroups of index p of A_(3)-groups.

A classification of some regular p-groups and its applications

In this paper we classify regular p-groups with type invariants (e, 1, 1, 1) for e ≥ 2 and (1, 1, 1, 1, 1). As a by-product, we give a new approach to the classification of groups of order p5, p ≥ 5 a prime.

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.

Finite p-groups all of whose proper subgroups have small derived subgroups

Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.

Finite p-groups whose nonnormal subgroups have orders at most p^3

We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, 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.

On Two Classes of Finite Inseparable p-Groups

A finite group is inseparable, it does not split over any proper nontrivial normal subgroup; that is, if it has no nontrivial semidirect product decompositions. This paper investigates two classes of finite inseparable p-groups and, for p ≥ 3, establishes a necessary and sufficient condition for insep- arability.