eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
1
8
10.22108/ijgt.2014.2937
2937
Faithful real representations of cyclically pinched one-relator groups
Benjamin Fine
fine@fairfield.edu
1
Martin Kreuzer
martin.kreuzer@uni-passau.de
2
Gerhard Rosenberger
gerhard.rosenberger@math.uni-hamburg.de
3
Faireld University
Universitat Passau
University of Hamburg
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
hyperbolic group
limit group
faithful representation
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
9
16
10.22108/ijgt.2014.2968
2968
Groups with minimax commutator subgroup
Francesco de Giovanni
degiovan@unina.it
1
Marco Trombetti
marco.trombetti@unina.it
2
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
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
minimax group
commutator subgroup
torsion-free rank
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
17
30
10.22108/ijgt.2014.2984
2984
All simple groups with order from 1 million to 5 million are efficient
Colin Campbell
cmc@st-andrews.ac.uk
1
George Havas
georgehavas@gmail.com
2
Colin Ramsay
cram@itee.uq.edu.au
3
Edmund Robertson
efr@st-andrews.ac.uk
4
School of Mathematics and Statistics, University of St Andrews
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
School of Mathematics and Statistics, University of St Andrews
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
Efficient presentations
simple groups
coset enumeration
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
31
56
10.22108/ijgt.2014.2993
2993
Paraunitary matrices and group rings
Barry Hurley
barryj_2001@yahoo.co.uk
1
Ted Hurley
ted.hurley@nuigalway.ie
2
NUI, Galway
National University of Ireland Galway
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
paraunitary
idempotent
multidimensional
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
57
64
10.22108/ijgt.2014.3225
3225
Co-prolongations of a group extension
Nguyen Tien Quang
1
Doan Trong Tuyen
2
Nguyen Thi Thu Thuy
3
Hanoi National University of Education
National Economics University
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.
http://ijgt.ui.ac.ir/article_3225_cf176c576d10ffbb3a9c575f460e02e0.pdf
group extension
cohomology of groups
prolongation
obstruction
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2014-03-01
3
1
65
72
10.22108/ijgt.2014.3511
3511
Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
Reza Orfi
1
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 $xneq y$.
http://ijgt.ui.ac.ir/article_3511_4929283f277e00c3ce2dd11ff44df080.pdf
p-group
AC-group
Pairwise non-commuting elements