University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
Faithful real representations of cyclically pinched one-relator groups
1
8
EN
Benjamin
Fine
Faireld University
fine@fairfield.edu
Martin
Kreuzer
Universitat Passau
martin.kreuzer@uni-passau.de
Gerhard
Rosenberger
University of Hamburg
gerhard.rosenberger@math.uni-hamburg.de
In [4,5] using faithful complex representations of cyclically pinched and conjugacy pinched one-relator groups we proved that any limit group has a faithful representation in $PSL(2,C)$. Further this representation can be effectively constructed using the JSJ decomposition. In this note we show that any hyperbolic cyclically pinched one-relator group with maximal amalgamated subgroups in each factor has a 2-dimensional faithful real representation.
hyperbolic group,limit group,faithful representation
http://ijgt.ui.ac.ir/article_2937.html
http://ijgt.ui.ac.ir/article_2937_cdb4e12ae05d8b93eb4fcc2c5e574b2b.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
Groups with minimax commutator subgroup
9
16
EN
Francesco
de Giovanni
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
degiovan@unina.it
Marco
Trombetti
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
marco.trombetti@unina.it
A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of $G$ has finite rank. It is proved here that if $G$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup, then also the commutator subgroup $G'$ of $G$ is minimax. A corresponding result is proved for groups in which the commutator subgroup of every proper subgroup has finite torsion-free rank.
minimax group,commutator subgroup,torsion-free rank
http://ijgt.ui.ac.ir/article_2968.html
http://ijgt.ui.ac.ir/article_2968_a0361dfd4b08b2933ad65f68ad95fcd2.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
All simple groups with order from 1 million to 5 million are efficient
17
30
EN
Colin
M.
Campbell
School of Mathematics and Statistics, University of St Andrews
cmc@st-andrews.ac.uk
George
Havas
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
georgehavas@gmail.com
Colin
Ramsay
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
cram@itee.uq.edu.au
Edmund
F.
Robertson
School of Mathematics and Statistics, University of St Andrews
efr@st-andrews.ac.uk
There is much interest in finding short presentations for the finite simple groups. Indeed it has been suggested that all these groups are efficient in a technical sense. In previous papers we produced nice efficient presentations for all except one of the simple groups with order less than one million. Here we show that all simple groups with order between $1$ million and $5$ million are efficient by giving efficient presentations for all of them. Apart from some linear groups these results are all new. We also show that some covering groups and some larger simple groups are efficient. We make substantial use of systems for computational group theory and, in particular, of computer implementations of coset enumeration to find and verify our presentations.
Efficient presentations,simple groups,coset enumeration
http://ijgt.ui.ac.ir/article_2984.html
http://ijgt.ui.ac.ir/article_2984_1966833cf149fe7e096cd9874914cd5c.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
Paraunitary matrices and group rings
31
56
EN
Barry
Hurley
NUI, Galway
barryj_2001@yahoo.co.uk
Ted
Hurley
National University of Ireland Galway
ted.hurley@nuigalway.ie
Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.
paraunitary,idempotent,multidimensional
http://ijgt.ui.ac.ir/article_2993.html
http://ijgt.ui.ac.ir/article_2993_caea049cd9d09fef8835afb8db2cf879.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
Co-prolongations of a group extension
57
64
EN
Nguyen Tien
Quang
Hanoi National University of Education
Doan Trong
Tuyen
National Economics University
Nguyen Thi Thu
Thuy
Hanoi University of Science and Technology
The aim of this paper is to study co-prolongations of central extensions. We construct the obstruction theory for co-prolongations and classify the equivalence classes of these by kernels of homomorphisms between 2-dimensional cohomology groups of groups.
group extension,cohomology of groups,prolongation,obstruction
http://ijgt.ui.ac.ir/article_3225.html
http://ijgt.ui.ac.ir/article_3225_cf176c576d10ffbb3a9c575f460e02e0.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
3
1
2014
03
01
Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
65
72
EN
Reza
Orfi
University of Arak
Let $G$ be a non-abelian group of order $p^n$, where $nleq 5$ in which $G$ is not extra special of order $p^5$. In this paper we determine the maximal size of subsets $X$ of $G$ with the property that $xyneq yx$ for any $x,y$ in $X$ with $xneq y$.
p-group,AC-group,Pairwise non-commuting elements
http://ijgt.ui.ac.ir/article_3511.html
http://ijgt.ui.ac.ir/article_3511_4929283f277e00c3ce2dd11ff44df080.pdf