*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C.
Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson
(Houston), J. Nagata (Osaka), V. I. Paulsen (Houston), G. Pisier (College
Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

**Wickless, William, **University of Connecticut, Storrs, CT 06269 (wickless@math.uconn.edu).

Multi-Isomorphism for Quotient
Divisible Groups,
pp. 1-20.

ABSTRACT.
Abelian groups A, B are called multi-isomorphic if A^{n} is isomorphic
to B^{n} for all natural numbers n>1. In a series of papers, K. O'Meara
and C. Vinsonhaler have studied this notion for torsion-free groups of finite
rank (tffr ). We study multi-isomorphism in the class of quotient divisible (qd)
abelian groups. A reduced abelian group G is qd if it contains a finite rank
free subgroup F such that G/F is a divisible torsion group. Multi-isomorphism
for qd groups shares some properties with those discovered by O'Meara and
Vinsonhaler in the tffr case, but also has some interesting differences.

**Coy L. May** and **Jay Zimmerman, **Department of Mathematics,
Towson University, 8000 York Road, Towson, Maryland 21252 ( cmay@towson.edu),
(jzimmerman@towson.edu).

The Groups of Strong Symmetric
Genus 4, pp. 21-35.

ABSTRACT.
Let G be a finite group. The strong symmetric genus is the minimum genus of any
Riemann surface on which G acts preserving orientation. The groups of strong
symmetric genus 3 or less have been classified. Here we classify the groups of
strong symmetric genus four. There are exactly ten such groups; eight of these
are automorphism groups of regular maps of genus 4.

We also consider non-abelian p-groups that have an element of maximal possible
order. We complete the determination of the strong symmetric genus of each
p-group with this property. Conversely, the non-abelian 2-groups of even
positive strong symmetric genus have an element of maximum possible order.
Further, we establish that for an odd prime p, the strong symmetric genus of a
non-abelian p-group is congruent to one modulo a power of p.

**Tetsuya Hosaka, ** Department of Mathematics, Utsunomiya University,
Utsunomiya, 321-8505, Japan (hosaka@cc.utsunomiya-u.ac.jp).

Strong reflection rigidity of
Coxeter systems of dihedral groups, pp. 37-41.

ABSTRACT.
In this paper, we study strong rigidity and strong reflection rigidity of
Coxeter systems of dihedral groups. We show that the Coxeter system of the
dihedral group D_{n} of order 2n is strongly reflection rigid if and
only if n∈{2,3,4,6}, and that the dihedral Coxeter group D_{n} is
strongly rigid if and only if n∈{3,4}.

**Florian Kainrath, **
Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstrasse 36,
A-8010 Graz, Austria (florian.kainrath@uni-graz.at).

Elasticity of Finitely
Generated Domains,
pp. 43-64.

ABSTRACT.
Let R be an atomic domain. Then every non unit a of R may be written as a
product of irreducibles. Let L(a) resp. l(a) denote the longest resp. shortest
length of all such factorizations of a. The elasticity of R is defined as the
supremum of all quotients L(a)/l(a), where a runs through all non units of R. In
this paper we characterize those finitely generated domains having finite
elasticity.

**Chatham, R. Douglas**, Morehead State University, Morehead, KY 40351 (d.chatham@moreheadstate.edu),
and **Dobbs, David E.**, University of Tennessee, Knoxville, TN 37996-1300 (dobbs@math.utk.edu).

On Open Ring Pairs Of
Commutative Rings,
pp. 65-74.

ABSTRACT.
If T is an integral commutative extension of a ring R such that R is an open
ring, R[a, b] is a going-down ring for each a, b in T and T is semiquasilocal,
then each ring contained between R and T is an open ring. An example is given to
show that the "semiquasilocal" hypothesis cannot be deleted. If T is a
commutative ring containing a ring R such that R[a, b] is an open ring for each
a, b in T, then (R, T) is an INC-pair (equivalently, a residually algebraic
pair).

**Hedayat, Sina, ** University of Kerman, Kerman, Iran, and ** Nekooei,
Reza, **University of Kerman, Kerman, Iran (rnekooei@mail.uk.ac.ir).

Characterization of Prime
Submodules of a Finitely Generated Free Module over a PID,
pp. 75-85.

ABSTRACT.
In this paper we discuss properties of a set of prime submodules of a finitely
generated free module F over a UFD and characterize the prime submodules of a
free module of finite rank over a PID. Finally; we obtain the radical of a
cyclic submodule of F and the radical of a submodule of a rank 2 free module
over a PID.

**Daciberg Goncalves, ** Departamento de Matematica - IME - USP, Caixa Postal
66.281 - CEP 05311-970, São Paulo- SP, Brasil (dlgoncal@ime.usp.br) , and **
João Peres Vieira, ** Departamento de Matematica -IGCE - UNESP, Caixa Postal
178 - CEP 13500-230, Rio Claro - SP, Brasil (jpvieira@rc.unesp.br).

Free Actions of Abelian
P-Groups on the N -Torus , pp 87-101.

ABSTRACT.
In this work we make some contributions to the theory of actions of abelian
p-groups on the n-Torus T^{n}. Set H ≈ (Z_{pk1})^{h1}
× (Z_{pk2})^{h2} × … × (Z_{pkr})^{hr},
r ≥ 1, k_{1} ≥ k_{2} ≥ … ≥ k_{r} ≥ 1, p prime. Suppose
that the group H acts freely on T^{n} and the induced representation on
Π_{1}(T^{n}) ≈ Z^{n} is faithful and has first Betti
number b. We show that the numbers n, p, b, k_{i} and h_{i},
(i=1,…,r) satisfy some relation. In particular, when H ≈ (Z_{p})^{h},
the minimum value of n is Φ(p)+b when b ≥ 1. Also when H ≈ Z_{pk1}
× Z_{p} the minimum value of n is Φ(p^{k1})+p-1+b
for b ≥ 1. Here Φ denotes the Euler function.

**Juan Climent Vidal,** and **Juan Soliveres Tur, **Universidad de
Valencia, Departamento de Lógica y Filosofía de la Ciencia, E-46071 Valencia,
Spain. (juan.b.climent@uv.es), (juan.soliveres@uv.es).

The Completeness Theorem for
Monads in Categories of Sorted Sets, pp. 103-129.

ABSTRACT.
Birkhoff's completeness theorem of equational logic asserts the coincidence of
the model-theoretic and proof-theoretic consequence relations. Goguen and
Meseguer, giving a sound and adequate system of inference rules for finitary
many-sorted equational deduction, generalized the completeness theorem of
Birkhoff to the completeness of finitary many-sorted equational logic and
provided simultaneously a full algebraization of finitary many-sorted equational
deduction. In this paper, after defining the concepts of equational class and
equational theory for a monad in a category of sorted sets and the concept of
projective limit-compatible congruence on a category, we prove that the lattice
of product-compatible congruences on the dual of the Kleisli category of a monad
in a category of sorted sets is identical to the lattice of equational theories
for the same monad. In this way we obtain a completeness theorem for monads in
categories of sorted sets, and therefore independent of any explicit syntactical
representation of the relevant concepts, that generalizes the completeness
theorem of Goguen-Meseguer and provides a full categorization of many-sorted
equational deduction.

**Xiaohuan Mo,** LMAM, School of Mathematical Sciences, Peking University,
Beijing 100871, People's Republic of China (moxh@pku.edu.cn).

On the Flag Curvature of a Finsler
Space with Constant S-Curvature , pp. 131-144.

ABSTRACT.
By establishing the intrinsic relation between the S-curvature and the flag
curvature we investigate the Finsler spaces with constant S-curvature. In
particular, we show that any Finsler space of scalar curvature and constant
S-curvature is a constant curvature space if its dimension ≥3

**Ronald A. Walton, ** 1671 Via Rancho, San Lorenzo, CA 94580
(rwsailor@mac.com).

A Symmetric Hyperbolic Structure
for Isentropic Relativistic Perfect Fluids, pp. 145-160.

ABSTRACT.
The dependent variables of an isentropic, relativistic perfect fluid can be
consolidated into a generalized velocity vector field equal to the fluid's
relativistic velocity vector field divided pointwise by the value of the fluid's
specific enthalpy. The equations of motion for an isentropic, relativistic
perfect fluid then become a quasilinear, first order, symmetric system of
partial differential equations, equivalent to local energy and momentum
conservation in the fluid. Furthermore, these equations of motion are symmetric
hyperbolic wherever the material density of the fluid is positive and the speed
of sound in the fluid does not exceed the speed of light. Two applications of
these equations are presented. First, the characteristic hypersurfaces of an
isentropic, relativistic perfect fluid are proven to consist of (1) timelike
hypersurfaces generated by the fluid streamlines and (2) nonspacelike, conical
hypersurfaces defined by the propagation of sound waves. And second, the
equations of motion for a self-gravitating, isentropic, relativistic perfect
fluid are proven to be equivalent to a quasilinear, first order, symmetric
hyperbolic system if the spacetime coordinates are constrained to be harmonic.

**Andrew Przeworski**
Dept. of Mathematics , University of Texas, Austin, TX 78712
(prez@math.utexas.edu).

Balls in Hyperbolic
3-Manifolds, pp. 161-171.

ABSTRACT.
We show that in a closed orientable hyperbolic 3-manifold, any maximal embedded
tube of radius r contains a ball of a certain radius. We then use the fact that
most closed orientable hyperbolic 3-manifolds contain tubes of radius (log 3)/2
to provide a universal lower bound on the radius of the ball.

**Ivansic, Ivan, **
University of Zagreb, FER, Unska 3, 10000 Zagreb, Croatia
(ivan.ivansic@fer.hr),
and **Milutinovic, Uros, **
University of Maribor, PEF, Koroska 160, 2000 Maribor, Slovenia
(uros.milutinovic@uni-mb.si).

The pointed version of
Lipscomb's embedding theorem, pp. 173-192.

ABSTRACT.
Let S(t) be the generalized Sierpinski curve, which is naturally identified with
Lipscomb's space J(t).

Then for any n-dimensional metric space X of weight t there is an embedding of X
into L_{n}(t), where L_{n}(t) is the subset of S(t)^{n+1}
of all points having at least one so called irrational coordinate. Here we prove
that this embedding may be chosen in such a way that its value at a certain
point (the base point) is given in advance. In fact, we prove a stronger result
that the values of the embedding may be given in advance at any finite set of
points of X.

**Yun Ziqiu,** Department of Mathematics, Suzhou University, 215006
P.R.China (yunziqiu@public1.sz.js.cn).

On Closed Mappings, pp.
193-197.

ABSTRACT.
In the present paper, some sufficient conditions for closed mappings to be
peripherally compact are given and a problem of Y. Tanaka and C. Liu is
answered.

**Gauld, David, **Department of Mathematics, University of Auckland, PB
92019, Auckland, New Zealand
(gauld@math.auckland.ac.nz), and **Mynard, Frédéric, **Department of
Mathematical Sciences, Georgia Southern University, 203 Georgia Ave. Room 3038,
Statesboro, GA 30460-8093
(fmynard@georgiasouthern.edu ).

Metrisability of Manifolds in
Terms of Function Spaces, pp.199-214.

ABSTRACT.
Both internal and external new criteria of metrisability of a topological
manifold are obtained.

The external ones involve topological properties of the space of real-valued
continuous functions over the manifold, endowed either with the topology of
pointwise convergence or with the compact-open topology.

** Arhangel'skii, Alexander, **Ohio University, Athens, Ohio, 45701
(arhangel@math.ohiou.edu).

Quotients with respect to
Locally Compact Subgroups, pp. 215-226.

ABSTRACT.
We establish that, for any locally compact subgroup H of a topological group G,
the natural quotient mapping of G onto the quotient space G/H is locally
perfect, that is, the restriction of it to the closure of some open set is an
open mapping with compact fibers. We derive from this that many important
topological invariants are transfered from the space G/H to G when H is locally
compact.

**Mou, Lei,** Mathematics Department, Capital Normal University, Beijing,
100037 China (Current address: Faculty of Education, Shizuoka University, Ohya,
Shizuoka, 422-8529 Japan), and **Ohta, Haruto,** Faculty of Education,
Shizuoka University, Ohya, Shizuoka, 422-8529 Japan
(echohta@ipc.shizuoka.ac.jp).

Sharp Bases and Mappings, pp.
227-238.

ABSTRACT.
Let S be the class of spaces with a sharp base in the sense of B. Alleche, A. V.
Arhangel'skii and J. Calbrix (2000). A map f is called boundedly finite-to-one
(resp. k-to-one) if there is a natural number k such that each fiber of f
consists of at most (resp. exactly) k many points. Answering a question asked by
C. Good, R. W. Knight and A. M. Mohamad (2002), we prove: (1) The image of a
space in S under a perfect map or an open finite-to-one map is not necessarily
in S, but every open boundedly finite-to-one image of a space in S is in S. (2)
The preimage of a space in S under an open closed boundedly finite-to-one map is
not necessarily in S, but every open k-to-one preimage of a space in S is in S.

**Miroslaw Sobolewski, **Instytut Matematyki, Faculty of Mathematics,
Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
(msobol@mimuw.edu.pl).

A Curve with the Fixed
Point Property whose Cylinder admits a Fixed Point Free Map, pp. 239-253.

ABSTRACT.
We construct a curve, i.e., a one-dimensional metric continuum, which has the
fixed point property but its product by the interval admits a fixed point free
mapping. This answers a question by R.H. Bing.

**Patton, Linda J.**, Mathematics Department, California Polytechnic State
University, San Luis Obispo, CA 93402 (lpatton@calpoly.edu), and
**Robbins, Marian E.,** Mathematics Department, Bellarmine University, 2001
Newburg Road, Louisville, KY 40205 (mrobbins@bellarmine.edu).

Composition Operators that are
M-isometries, pp. 255-265.

ABSTRACT.
The results in this paper show that on many Hilbert spaces of analytic
functions, including Hardy spaces on the ball and polydisc and standard weighted
Bergman spaces on the disk, the only m-isometric composition operators are
isometries. Necessary conditions for the symbols of m-isometric composition
operators on Dirichlet space are also derived. Finally, it is shown that for
symbols with fixed point in the unit disk, the associated composition operator
has an m-isometric adjoint if and only if the symbol is an automorphism that
fixes the origin.

**Razvan Anisca, ** Department of Mathematical Sciences, Lakehead
University, 955 Oliver Road, Thunder Bay, Ontario Canada, P7B
5E1(razvan.anisca@lakeheadu.ca), **Adi Tcaciuc, **Department of Mathematical
and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G
2G1 (tcaciuc@math.ualberta.ca), and **Nicole Tomczak-Jaegermann, **
Department of Mathematical and Statistical Sciences, University of Alberta,
Edmonton, Alberta, Canada T6G 2G1 (nicole@ellpspace.math.ualberta.ca).

Structure of normed spaces with
extremal distance to the Euclidean space, pp. 267-283.

ABSTRACT.
It is shown that a finite dimensional Banach space has the Euclidean distance of
maximal order if and only if it contains a proportional dimensional subspace
(and a quotient of a subspace) of a very special form.

**Ignat, Radu, **École Normale Supérieure, Paris, France
(Radu.Ignat@ens.fr).

On an Open Problem about how to
Recognize Constant Functions, pp. 285-304.

ABSTRACT.
In this paper we generalize a result of Bourgain, Brezis and Mironescu about how
to recognize constant functions; its motivation comes from the uniqueness of the
lifting in some Sobolev spaces. We also answer to an open question raised by
Brezis concerning the previous result.