eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
1
4
10.22108/ijgt.2016.21237
21237
On groups with a restriction on normal subgroups
Alessio Russo
alessio.russo@unina2.it
1
Seconda Universit&agrave; di Napoli
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).
http://ijgt.ui.ac.ir/article_21237_404c5b3acc80442c0389dbab78844bf3.pdf
normal subgroup
soluble group
isomorphism class
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
5
16
10.22108/ijgt.2016.21235
21235
Countably recognizable classes of groups with restricted conjugacy classes
Francesco de Giovanni
degiovan@unina.it
1
Marco Trombetti
marco.trombetti@unina.it
2
Dipartimento di Matematica e Applicazioni - University of Napoli &quot;Federico II&quot;
Universita di Napoli Federico II,
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.
http://ijgt.ui.ac.ir/article_21235_894f1a96aa9ff81f3b1db138105bf512.pdf
conjugacy class
countable recognizability
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
17
21
10.22108/ijgt.2017.21220
21220
Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements
Andrea Lucchini
lucchini@math.unipd.it
1
Dipartimento di Matematica
Università di Padova
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.
http://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdf
Character degrees
class sizes
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
23
36
10.22108/ijgt.2017.21216
21216
Conjugacy classes contained in normal subgroups: an overview
Antonio Beltran
abeltran@mat.uji.es
1
Maria Jose Felipe
mfelipe@mat.upv.es
2
Carmen Melchor
cmelchor@uji.es
3
Universitat Jaume I
Universitat Politécnica de València
Universitat Jaume I
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.
http://ijgt.ui.ac.ir/article_21216_521a00edf9dcb7b91295b2b081a9a468.pdf
Conjugacy classes
normal subgroups
graphs
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
37
50
10.22108/ijgt.2017.21674
21674
On the relationships between the factors of the upper and lower central series in some non-periodic groups
Martyn Dixon
mdixon@ua.edu
1
Leonid Kurdachenko
lkurdachenko@yahoo.com.ua
2
Igor Subbotin
isubboti@nu.edu
3
University of Alabama
National University of Dnepropetrovsk
National University
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.
http://ijgt.ui.ac.ir/article_21674_99f61bdccf031d8e387d46fc8009fb86.pdf
finite rank
torsion-free rank
section $p$-rank
generalized radical group
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
51
56
10.22108/ijgt.2017.21215
21215
Regular subgroups, nilpotent algebras and projectively congruent matrices
Marco Pellegrini
marco.a.pellegrini@gmail.com
1
Universit&agrave; Cattolica del Sacro Cuore
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.
http://ijgt.ui.ac.ir/article_21215_2ad48b9247fe4edac37cbe792dfa993c.pdf
Regular subgroup
nilpotent algebra
congruent matrices
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2018-03-01
7
1
57
64
10.22108/ijgt.2016.21218
21218
On groups with two isomorphism classes of central factors
Serena Siani
ssiani@unisa.it
1
Universitamp;agrave; degli Studi di Salerno
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.
http://ijgt.ui.ac.ir/article_21218_ce8d518bf9ab00038546f615ced4d6d7.pdf
Center
Isomorphism types
locally finite groups
locally graded groups