@Article{Fine2014,
author="Fine, Benjamin
and Kreuzer, Martin
and Rosenberger, Gerhard",
title="Faithful real representations of cyclically pinched one-relator groups",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="1-8",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2014.2937",
url="http://ijgt.ui.ac.ir/article_2937.html"
}
@Article{deGiovanni2014,
author="de Giovanni, Francesco
and Trombetti, Marco",
title="Groups with minimax commutator subgroup",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="9-16",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2014.2968",
url="http://ijgt.ui.ac.ir/article_2968.html"
}
@Article{Campbell2014,
author="Campbell, Colin M.
and Havas, George
and Ramsay, Colin
and Robertson, Edmund F.",
title="All simple groups with order from 1 million to 5 million are efficient",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="17-30",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2014.2984",
url="http://ijgt.ui.ac.ir/article_2984.html"
}
@Article{Hurley2014,
author="Hurley, Barry
and Hurley, Ted",
title="Paraunitary matrices and group rings",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="31-56",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2014.2993",
url="http://ijgt.ui.ac.ir/article_2993.html"
}
@Article{Quang2014,
author="Quang, Nguyen Tien
and Tuyen, Doan Trong
and Thuy, Nguyen Thi Thu",
title="Co-prolongations of a group extension",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="57-64",
abstract="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.",
issn="2251-7650",
doi="10.22108/ijgt.2014.3225",
url="http://ijgt.ui.ac.ir/article_3225.html"
}
@Article{Orfi2014,
author="Orfi, Reza",
title="Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$",
journal="International Journal of Group Theory",
year="2014",
volume="3",
number="1",
pages="65-72",
abstract="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 $x\neq y$.",
issn="2251-7650",
doi="10.22108/ijgt.2014.3511",
url="http://ijgt.ui.ac.ir/article_3511.html"
}