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.     

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 ?ernikov p-群的结构.     

Connected components of the category of elementary abelian p-subgroups

We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank 2 in a finite p-group G, for an odd prime p. Namely, it is p if G has rank at least 3 and it is p+1 if G has rank 2. More precisely, if G has rank 2, there are exactly 1,2,p+1, or possibly 3 classes for some 3-groups of maximal nilpotency class.     

The automorphism group of a split metacyclic 2-group and some groups of crossed homomorphisms

In this paper we find the structure for the automorphism group of a split metacyclic 2-group G. It can be seen as a continuation of the paper (Curran in Arch. Math. 89 (2007), 10–23) and it makes it complete. We propose a different approach to the problem than in the paper (Curran in Arch. Math. 89 (2007), 10–23). Our intention is to show that apart from some cases of 2-groups AutG has a structure similar to that of a direct product of two groups with no common direct factor [which was considered in Bidwell, Curran, and McCaughan (Arch. Math. 86 (2006), 481–489)].      

The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.     

KK-groups for generalized operator algebras. I

Kasparov's bivariant K-theory is extended to inverse limits of C ^*-algebras. It is shown how to define the intersection product for algebras satisfying a separability condition and the properties of the product are explained. The Bott periodicity theorem is proved.     

KK-groups for generalized operator algebras. II

The extension of Kasparovs bivariant K-theory to inverse limits of C ^* -algebras admits exact Puppe sequences in both variables. Two exact sequences generalizing Milnor's lim-lim¹ sequences are established. For CW complexes the extended K-theory is representable K-theory.     

A Note on a Class of Factorized <Emphasis Type="Italic">p</Emphasis>-Groups

In this note we study finite p-groups G = AB admitting a factorization by an Abelian subgroup A and a subgroup B. As a consequence of our results we prove that if B contains an Abelian subgroup of index p ⁿ⁻¹ then G has derived length at most 2n.     

Regular submodules of torsion modules over a discrete valuation domain

A submodule W of a p-primary module M of bounded order is known to be regular if W and M have simultaneous bases. In this paper we derive necessary and sufficient conditions for regularity of a submodule.     

Characteristic properties of large subgroups in primary abelian groups

SupposeG is an arbitrary additively written primary abelian group with a fixed large subgroupL. It is shown thatG is (a) summable; (b) σ-summable; (c) a Σ-group; (d) p^ω+1-projecrive only when so isL. These claims extend results of such a kind obtained by Benabdallah, Eisenstadt, Irwin and Poluianov,Acta Math. Acad. Sci. Hungaricae (1970) and Khan,Proc. Indian Acad. Sci. Sect. A (1978).     

Multiple positive solutions for some p-Laplacian boundary value problems

This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian subject to one of the following boundary conditions: or where φ_p(s)=|s|^p−2s, p>1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.     

On the regular Sylow p-subgroups of Chevalley groups over \mathbb{Z}_{p^m }

We prove that a Sylow p-subgroup of the general linear group of dimension n over the residue ring modulo p ^m is regular for n ² < p and powerful if and only if n = 2 and m = 1. We obtain similar results for the Sylow p-subgroups of normal types over the same ring.     

A Classification of Regular p-Groups with Invariants (e, 2, 1)

The class of the regular p-groups is one of the important classes in p-groups. Not only it has many similar properties as abelian p-groups, but also many of the p-groups belong to this class. In this paper, using the algorithms for determining the isomorphic regular p-groups, we give a complete classification of the regular p-groups with e-invariants (e, 2, 1).Supported by SXYSF 991003.     

Formation and construction of shock for p -system

The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the starting point of the shock are also obtained     

Classifying cubic symmetric graphs of order 10p or 10p2

A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ⩾ 1 are classified when the fibre-preserving automorphism groups act arc-transitively. As an application of these results, all s-regular cubic graphs of order 10p or 10p ² are also classified for each s ⩾ 1 and each prime p, of which the proof depends on the classification of finite simple groups.     

Milnor K-Groups and Zero-Cycles on Products of Curves over p-Adic Fields

We investigate the Chow groups of zero cycles of products of curves over a p-adic field by means of the Milnor K-groups of their Jacobians as introduced by Somekawa. We prove some finiteness results for CH ₀(X)/m for X a product of curves over a p-adic field.     

Relative -difference sets in p-subgroups of

In this note, we study relative (p^a,p^b,p^a,p^a−b)-relative difference sets in certain p-subgroups of SL(n,K), K=F_q, where q is a prime power.     

On some exact sequences in the theory of cyclotomic fields

The purpose of this article is to show the existence of some exact sequences which relate the ideal class groups of cyclotomic fields to Gauss sums. These exact sequences imply the results of Hachimori, Ichimura and Beliaeva. Furthermore, we study the relations between the étale cohomology groups and some conjectures on cyclotomic fields.