@Article{Russo2015,
author="Russo, Alessio",
title="On central endomorphisms of a group",
journal="International Journal of Group Theory",
year="2015",
volume="4",
number="3",
pages="1-5",
abstract="Let $\Gamma$ be a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$, and assume that $Inn(G)\leq \Gamma$. An endomorphism $\sigma$ of $G$ is said to be $\Gamma$-central if $\sigma$ induces the the identity on the factor group $G/C_G(\Gamma)$. Clearly, if $\Gamma=Inn(G)$, then a $\Gamma$-central endomorphism is a central endomorphism. In this article the conditions under which a $\Gamma$-central endomorphism of a group is an automorphism are investigated.",
issn="2251-7650",
doi="10.22108/ijgt.2015.9970",
url="http://ijgt.ui.ac.ir/article_9970.html"
}
@Article{Stepanov2015,
author="Stepanov, Alexey",
title="Sandwich classification theorem",
journal="International Journal of Group Theory",
year="2015",
volume="4",
number="3",
pages="7-12",
abstract="The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups $F\le N$ of a group $G$ denote by $L(F,N)$ the set of all subgroups of $N$, containing $F$. Let $D$ be a subgroup of $G$. In this note we study the lattice $LL=L(D,G)$ and the lattice $LL'$ of subgroups of $G$, normalized by $D$. We say that $LL$ satisfies sandwich classification theorem if $LL$ splits into a disjoint union of sandwiches $L(F,N_G(F))$ over all subgroups $F$ such that the normal closure of $D$ in $F$ coincides with $F$. Here $N_G(F)$ denotes the normalizer of $F$ in $G$. A similar notion of sandwich classification is introduced for the lattice $LL'$. If $D$ is perfect, i.\,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for $LL$ and $LL'$ are equivalent. We also show how to find basic subroup $F$ of sandwiches for $LL'$ and review sandwich classification theorems in algebraic groups over rings.",
issn="2251-7650",
doi="10.22108/ijgt.2015.10515",
url="http://ijgt.ui.ac.ir/article_10515.html"
}
@Article{Pellegrini2015,
author="Pellegrini, Marco
and Tamburini, Maria",
title="Finite simple groups of low rank: Hurwitz generation and $(2,3)$-generation",
journal="International Journal of Group Theory",
year="2015",
volume="4",
number="3",
pages="13-19",
abstract="Let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $\le 7$ over an algebraically closed field $F$ of characteristic $p\geq 0$. We survey some recent results which lead to the complete list of the groups in this set which are $(2, 3, 7)$-generated and of those which are $(2,3)$-generated.",
issn="2251-7650",
doi="10.22108/ijgt.2015.10630",
url="http://ijgt.ui.ac.ir/article_10630.html"
}
@Article{Traustason2015,
author="Traustason, Gunnar",
title="The local nilpotence theorem for 4-Engel groups revisited",
journal="International Journal of Group Theory",
year="2015",
volume="4",
number="3",
pages="21-75",
abstract="The proof of the local nilpotence theorem for $4$-Engel groups was completed by G. Havas and M. Vaughan-Lee in 2005. The complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. In the process we are also able to make a few simplifications and in particular we are able to merge two of the key steps into one.",
issn="2251-7650",
doi="10.22108/ijgt.2015.5551",
url="http://ijgt.ui.ac.ir/article_5551.html"
}
@Article{Juhasz2015,
author="Juhasz, Arye",
title="Conjugacy in relatively extra-large Artin groups",
journal="International Journal of Group Theory",
year="2015",
volume="4",
number="3",
pages="77-117",
abstract="In this work we consider conjugacy of elements and parabolic subgroups in details, in a new class of Artin groups, introduced in an earlier work, which may contain arbitrary parabolic subgroups. In particular, we find algorithmically minimal representatives of elements in a conjugacy class and also an algorithm to pass from one minimal representative to the others.",
issn="2251-7650",
doi="10.22108/ijgt.2015.11019",
url="http://ijgt.ui.ac.ir/article_11019.html"
}