2018-08-19T17:23:48Z
http://ijgt.ui.ac.ir/?_action=export&rf=summon&issue=4092
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
On groups with a restriction on normal subgroups
Alessio
Russo
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).
normal subgroup
soluble group
isomorphism class
2018
03
01
1
4
http://ijgt.ui.ac.ir/article_21237_404c5b3acc80442c0389dbab78844bf3.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
Countably recognizable classes of groups with restricted conjugacy classes
Francesco
de Giovanni
Marco
Trombetti
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.
conjugacy class
countable recognizability
2018
03
01
5
16
http://ijgt.ui.ac.ir/article_21235_894f1a96aa9ff81f3b1db138105bf512.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements
Andrea
Lucchini
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.
Character degrees
class sizes
2018
03
01
17
21
http://ijgt.ui.ac.ir/article_21220_7d6849ef0c0f20d2874ee36c05cf3ef1.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
Conjugacy classes contained in normal subgroups: an overview
Antonio
Beltran
Maria
Jose Felipe
Carmen
Melchor
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.
Conjugacy classes
normal subgroups
graphs
2018
03
01
23
36
http://ijgt.ui.ac.ir/article_21216_521a00edf9dcb7b91295b2b081a9a468.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
On the relationships between the factors of the upper and lower central series in some non-periodic groups
Martyn
Dixon
Leonid
Kurdachenko
Igor
Subbotin
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.
finite rank
torsion-free rank
section $p$-rank
generalized radical group
2018
03
01
37
50
http://ijgt.ui.ac.ir/article_21674_99f61bdccf031d8e387d46fc8009fb86.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
Regular subgroups, nilpotent algebras and projectively congruent matrices
Marco
Pellegrini
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.
Regular subgroup
nilpotent algebra
congruent matrices
2018
03
01
51
56
http://ijgt.ui.ac.ir/article_21215_2ad48b9247fe4edac37cbe792dfa993c.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
1
On groups with two isomorphism classes of central factors
Serena
Siani
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.
Center
Isomorphism types
locally finite groups
locally graded groups
2018
03
01
57
64
http://ijgt.ui.ac.ir/article_21218_ce8d518bf9ab00038546f615ced4d6d7.pdf