On groups with a restriction on normal subgroups
Alessio
Russo
Seconda Universit&agrave; di Napoli
author
text
article
2018
eng
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).
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
1
4
http://ijgt.ui.ac.ir/article_21237_404c5b3acc80442c0389dbab78844bf3.pdf
dx.doi.org/10.22108/ijgt.2016.21237
Countably recognizable classes of groups with restricted conjugacy classes
Francesco
de Giovanni
Dipartimento di Matematica e Applicazioni - University of Napoli &quot;Federico II&quot;
author
Marco
Trombetti
Universita di Napoli Federico II,
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
5
16
http://ijgt.ui.ac.ir/article_21235_894f1a96aa9ff81f3b1db138105bf512.pdf
dx.doi.org/10.22108/ijgt.2016.21235
Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements
Andrea
Lucchini
Dipartimento di Matematica
Università di Padova
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
17
21
http://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdf
dx.doi.org/10.22108/ijgt.2017.21220
Conjugacy classes contained in normal subgroups: an overview
Antonio
Beltran
Universitat Jaume I
author
Maria
Jose Felipe
Universitat Politécnica de València
author
Carmen
Melchor
Universitat Jaume I
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
23
36
http://ijgt.ui.ac.ir/article_21216_521a00edf9dcb7b91295b2b081a9a468.pdf
dx.doi.org/10.22108/ijgt.2017.21216
On the relationships between the factors of the upper and lower central series in some non-periodic groups
Martyn
Dixon
University of Alabama
author
Leonid
Kurdachenko
National University of Dnepropetrovsk
author
Igor
Subbotin
National University
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
37
50
http://ijgt.ui.ac.ir/article_21674_99f61bdccf031d8e387d46fc8009fb86.pdf
dx.doi.org/10.22108/ijgt.2017.21674
Regular subgroups, nilpotent algebras and projectively congruent matrices
Marco
Pellegrini
Universit&agrave; Cattolica del Sacro Cuore
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
51
56
http://ijgt.ui.ac.ir/article_21215_2ad48b9247fe4edac37cbe792dfa993c.pdf
dx.doi.org/10.22108/ijgt.2017.21215
On groups with two isomorphism classes of central factors
Serena
Siani
Universitamp;agrave; degli Studi di Salerno
author
text
article
2018
eng
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.
International Journal of Group Theory
University of Isfahan
2251-7650
7
v.
1
no.
2018
57
64
http://ijgt.ui.ac.ir/article_21218_ce8d518bf9ab00038546f615ced4d6d7.pdf
dx.doi.org/10.22108/ijgt.2016.21218