Twisted conjugacy classes in saturated weakly branch groups

For a wide class of saturated weakly branch groups, including the (first) Grigorchuk group and the Gupta-Sidki group, we prove that the Reidemeister number of any automorphism is infinite.      

The Primitive Sharp Permutation Groups of Twisted Wreath Type

A permutation group G ≤ Sym(X) on a finite set X is sharp if |G|=∏ _l?L(G)(|X| ? l), where L(G) = {|fix(g)| | 1 ≠ g ? G}. We show that no finite primitive permutation groups of twisted wreath type are sharp.     

Twisted identities in Coxeter groups

Given a Coxeter system (W,S) equipped with an involutive automorphism θ, the set of twisted identities is

弱Hopf代数上的扭积

在弱Hopf代数上,定义了交叉积概念,并且得到了它的两种特殊形式,冲积和扭积．特别地,给出了扭积为弱Hopf代数的一个充要条件,推广了Hopf代数的相应结论．     

The conjugacy problem for Dehn twist automorphisms of free groups

A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of . Received: February 12, 1996.     

On the word problem and the conjugacy problem for groups of the formF/V(R)

LetF be a free group with at most countable system of free generators, letR be its normal subgroup recursively enumerable with respect to , and let be a variety of groups that differs from and for which the corresponding verbal subgroupV of the free group of countable rank is recursive. It is proved that the word problem inF/V(R) is solvable if and only if this problem is solvable inF/R, and if , then there exists anR such, that the conjugacy problem inF/R is solvable, but this problem is unsolvable inF/V(R) for any Abelian variety (all algorithmic problems are regarded with respect to the images of under the corresponding natural epimorphisms). Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 3–9, January, 1997. Translated by M. I. Anokhin     

Twisted tensor product codes

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction.      

扭曲Smash积的辫Monoidal范畴与辫Monoidal范畴上的扭曲Smash积

得出了扭曲Ｓｍａｓｈ积模范畴Ａ＊ＨＭ是辫ｍｏｎｏｉｄａｌ范畴的一个充要条件;进一步讨论了与范畴Ａ—ＨＭ等价的范畴,引进了广义Ｙｅｔｔｅｒ－Ｄｒｉｎｆｅｌｄ范畴ＨＭＣ;最后,给出了辫Ｍｏｎｏｉｄａｌ范畴上扭曲Ｓｍａｓｈ积构成Ｈｏｐｆ代数充要的条件,这些结果统一了量子群中许多重要结论。     

On the width in free products with amalgamation

In this paper, the problem of finite width for free products of groups with amalgamated subgroup is considered. Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 353–359, September, 2000.     

On conjugacy class sizes of primary and biprimary elements of a finite group

Let m, n > 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1,m, n,mn}.     

On a Spectral Sequence for Twisted Cohomologies

Let(Ω*(M), d) be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex(Ω*(M), d + H∧) and its associated twisted de Rham cohomology H*(M, H). The authors show that there exists a spectral sequence {Ep,qr, dr} derived from the filtration Fp(Ω*(M)) = i≥pΩi(M) of Ω*(M), which converges to the twisted de Rham cohomology H*(M, H). It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well,which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.     

Twisted conjugacy in braid groups

In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u, υ ∈ B _n and an automorphism φ ∈ Aut(B _n ), decides whether υ = (φ(x))^?1 ux for some x ∈ B _n . As a corollary, we deduce that each group of the form B _n ? H, a semidirect product of the braid group B _n by a torsion-free hyperbolic group H, has solvable conjugacy problem.     

Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ? H and L-R smash product A?H, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in Brzeziński and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A ? H is isomorphic to A?H as Hopf quasigroups.     

Twisted product and cohomology

LetH be a Hopf algebra,H ₁ be a sub-Hopf algebra ofH, H ₂ be the quotient Hopt algebra ofH modularH ₁. This paper gives a simplified complex by defining a new base for the cobar complex and proves that the cobar complex ofH has the same cohomology algebra with a twisted product of the cobar complexes ofH ₁ andH ₂. Supported by National Natural Science Foundation of China     

Cyclic conjugacy separability and conjugacy separability of certain HNN extensions

Abstract

In this note, we give a criterion for certain HNN extensions of cyclic conjugacy separable (respectively conjugacy separable) groups with infinite cyclic associated subgroups to be again cyclic conjugacy separable (respectively conjugacy separable).

Communicated by Alexander Olshanskii     

conjugacy of 1-d diffeomorphisms with periodic points

It is shown that the set of heteroclinic orbits between two periodic orbits of saddle-node type induces functional moduli which are completely contained in a new `transition map'. For one-dimensional diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are conjugated if and only if the transition maps of their heteroclinic orbits are the same. An equivalent transition map is given for diffeomorphisms with hyperbolic periodic points, and it is shown that this transition map is an invariant of conjugation. However, in this case the transition map alone is sufficient to guarantee conjugacy only in a limited sense.