ORIGINAL_ARTICLE
Faithful real representations of cyclically pinched one-relator groups
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.
http://ijgt.ui.ac.ir/article_2937_cdb4e12ae05d8b93eb4fcc2c5e574b2b.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
1
8
10.22108/ijgt.2014.2937
hyperbolic group
limit group
faithful representation
Benjamin
Fine
fine@fairfield.edu
true
1
Faireld University
Faireld University
Faireld University
AUTHOR
Martin
Kreuzer
martin.kreuzer@uni-passau.de
true
2
Universitat Passau
Universitat Passau
Universitat Passau
AUTHOR
Gerhard
Rosenberger
gerhard.rosenberger@math.uni-hamburg.de
true
3
University of Hamburg
University of Hamburg
University of Hamburg
LEAD_AUTHOR
ORIGINAL_ARTICLE
Groups with minimax commutator subgroup
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.
http://ijgt.ui.ac.ir/article_2968_a0361dfd4b08b2933ad65f68ad95fcd2.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
9
16
10.22108/ijgt.2014.2968
minimax group
commutator subgroup
torsion-free rank
Francesco
de Giovanni
degiovan@unina.it
true
1
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
LEAD_AUTHOR
Marco
Trombetti
marco.trombetti@unina.it
true
2
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
AUTHOR
ORIGINAL_ARTICLE
All simple groups with order from 1 million to 5 million are efficient
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.
http://ijgt.ui.ac.ir/article_2984_1966833cf149fe7e096cd9874914cd5c.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
17
30
10.22108/ijgt.2014.2984
Efficient presentations
simple groups
coset enumeration
Colin
Campbell
cmc@st-andrews.ac.uk
true
1
School of Mathematics and Statistics, University of St Andrews
School of Mathematics and Statistics, University of St Andrews
School of Mathematics and Statistics, University of St Andrews
AUTHOR
George
Havas
georgehavas@gmail.com
true
2
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
LEAD_AUTHOR
Colin
Ramsay
cram@itee.uq.edu.au
true
3
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
AUTHOR
Edmund
Robertson
efr@st-andrews.ac.uk
true
4
School of Mathematics and Statistics, University of St Andrews
School of Mathematics and Statistics, University of St Andrews
School of Mathematics and Statistics, University of St Andrews
AUTHOR
ORIGINAL_ARTICLE
Paraunitary matrices and group rings
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.
http://ijgt.ui.ac.ir/article_2993_caea049cd9d09fef8835afb8db2cf879.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
31
56
10.22108/ijgt.2014.2993
paraunitary
idempotent
multidimensional
Barry
Hurley
barryj_2001@yahoo.co.uk
true
1
NUI, Galway
NUI, Galway
NUI, Galway
AUTHOR
Ted
Hurley
ted.hurley@nuigalway.ie
true
2
National University of Ireland Galway
National University of Ireland Galway
National University of Ireland Galway
LEAD_AUTHOR
ORIGINAL_ARTICLE
Co-prolongations of a group extension
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.
http://ijgt.ui.ac.ir/article_3225_cf176c576d10ffbb3a9c575f460e02e0.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
57
64
10.22108/ijgt.2014.3225
group extension
cohomology of groups
prolongation
obstruction
Nguyen Tien
Quang
true
1
Hanoi National University of Education
Hanoi National University of Education
Hanoi National University of Education
AUTHOR
Doan Trong
Tuyen
true
2
National Economics University
National Economics University
National Economics University
AUTHOR
Nguyen Thi Thu
Thuy
true
3
Hanoi University of Science and Technology
Hanoi University of Science and Technology
Hanoi University of Science and Technology
AUTHOR
ORIGINAL_ARTICLE
Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
Let $G$ be a non-abelian group of order $p^n$, where $n\leq 5$ 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 $xy\neq yx$ for any $x,y$ in $X$ with $x\neq y$.
http://ijgt.ui.ac.ir/article_3511_4929283f277e00c3ce2dd11ff44df080.pdf
2014-03-01T11:23:20
2019-01-18T11:23:20
65
72
10.22108/ijgt.2014.3511
p-group
AC-group
Pairwise non-commuting elements
Reza
Orfi
true
1
University of Arak
University of Arak
University of Arak
AUTHOR