Faithful real representations of cyclically pinched one-relator groups
Benjamin
Fine
Faireld University
author
Martin
Kreuzer
Universitat Passau
author
Gerhard
Rosenberger
University of Hamburg
author
text
article
2014
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
1
8
http://ijgt.ui.ac.ir/article_2937_cdb4e12ae05d8b93eb4fcc2c5e574b2b.pdf
dx.doi.org/10.22108/ijgt.2014.2937
Groups with minimax commutator subgroup
Francesco
de Giovanni
Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
author
Marco
Trombetti
Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
author
text
article
2014
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
9
16
http://ijgt.ui.ac.ir/article_2968_a0361dfd4b08b2933ad65f68ad95fcd2.pdf
dx.doi.org/10.22108/ijgt.2014.2968
All simple groups with order from 1 million to 5 million are efficient
Colin
Campbell
School of Mathematics and Statistics, University of St Andrews
author
George
Havas
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
author
Colin
Ramsay
Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering,
The University of Queensland
author
Edmund
Robertson
School of Mathematics and Statistics, University of St Andrews
author
text
article
2014
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
17
30
http://ijgt.ui.ac.ir/article_2984_1966833cf149fe7e096cd9874914cd5c.pdf
dx.doi.org/10.22108/ijgt.2014.2984
Paraunitary matrices and group rings
Barry
Hurley
NUI, Galway
author
Ted
Hurley
National University of Ireland Galway
author
text
article
2014
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
31
56
http://ijgt.ui.ac.ir/article_2993_caea049cd9d09fef8835afb8db2cf879.pdf
dx.doi.org/10.22108/ijgt.2014.2993
Co-prolongations of a group extension
Nguyen Tien
Quang
Hanoi National University of Education
author
Doan Trong
Tuyen
National Economics University
author
Nguyen Thi Thu
Thuy
Hanoi University of Science and Technology
author
text
article
2014
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
57
64
http://ijgt.ui.ac.ir/article_3225_cf176c576d10ffbb3a9c575f460e02e0.pdf
dx.doi.org/10.22108/ijgt.2014.3225
Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
Reza
Orfi
University of Arak
author
text
article
2014
eng
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 $x\neq y$.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
1
no.
2014
65
72
http://ijgt.ui.ac.ir/article_3511_4929283f277e00c3ce2dd11ff44df080.pdf
dx.doi.org/10.22108/ijgt.2014.3511