@Article{Russo2018,
author="Russo, Alessio",
title="On groups with a restriction on normal subgroups",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="1-4",
abstract="The structure of infinite groups in which every (proper) normal subgroup is the only one of its cardinality is investigated in the universe of groups without infinite simple sections. The corrisponding problem for finite soluble groups was considered by M. Curzio (1958).",
issn="2251-7650",
doi="10.22108/ijgt.2016.21237",
url="http://ijgt.ui.ac.ir/article_21237.html"
}
@Article{deGiovanni2018,
author="de Giovanni, Francesco
and Trombetti, Marco",
title="Countably recognizable classes of groups with restricted conjugacy classes",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="5-16",
abstract="A group class ${ X}$ is said to be countably recognizable if a group belongs to ${X}$ whenever all its countable subgroups lie in ${X}$. It is proved here that most of the relevant classes of groups defined by restrictions on the conjugacy classes are countably recognizable.",
issn="2251-7650",
doi="10.22108/ijgt.2016.21235",
url="http://ijgt.ui.ac.ir/article_21235.html"
}
@Article{Lucchini2018,
author="Lucchini, Andrea",
title="Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="17-21",
abstract="We prove that every finite group $G$ contains a three-generated subgroup $H$ with the following property: a prime $p$ divides the degree of an irreducible character of $G$ if and only if it divides the degree of an irreducible character of $H.$ There is no analogous result for the prime divisors of the sizes of the conjugacy classes.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21220",
url="http://ijgt.ui.ac.ir/article_21220.html"
}
@Article{Beltran2018,
author="Beltran, Antonio
and Jose Felipe, Maria
and Melchor, Carmen",
title="Conjugacy classes contained in normal subgroups: an overview",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="23-36",
abstract="We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21216",
url="http://ijgt.ui.ac.ir/article_21216.html"
}
@Article{Dixon2018,
author="Dixon, Martyn
and Kurdachenko, Leonid
and Subbotin, Igor",
title="On the relationships between the factors of the upper and lower central series in some non-periodic groups",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="37-50",
abstract="This paper deals with the mutual relationships between the factor group $G/\zeta(G)$ (respectively $G/\zeta_k(G)$) and $G'$ (respectively $\gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$). It is proved that if $G/\zeta(G)$ (respectively $G/\zeta_k(G)$) has finite $0$-rank, then $G'$ (respectively $\gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$) also have finite $0$-rank. Furthermore, bounds for the $0$-ranks of $G', \gamma_{k+1}(G)$ and $G^{\mathfrak{N}}$ are obtained.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21674",
url="http://ijgt.ui.ac.ir/article_21674.html"
}
@Article{Pellegrini2018,
author="Pellegrini, Marco",
title="Regular subgroups, nilpotent algebras and projectively congruent matrices",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="51-56",
abstract="In this paper we highlight the connection between certain classes of regular subgroups of the affine group $AGL_n(F)$, $F$ a field, and associative nilpotent $F$-algebras of dimension $n$. We also describe how the classification of projective congruence classes of square matrices is equivalent to the classification of regular subgroups of particular shape.",
issn="2251-7650",
doi="10.22108/ijgt.2017.21215",
url="http://ijgt.ui.ac.ir/article_21215.html"
}
@Article{Siani2018,
author="Siani, Serena",
title="On groups with two isomorphism classes of central factors",
journal="International Journal of Group Theory",
year="2018",
volume="7",
number="1",
pages="57-64",
abstract="The structure of groups which have at most two isomorphism classes of central factors ($B_2$-groups) are investigated. A complete description of $B_2$-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble $B_2$-groups. Also structural information about insoluble $B_2$-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition.",
issn="2251-7650",
doi="10.22108/ijgt.2016.21218",
url="http://ijgt.ui.ac.ir/article_21218.html"
}