2018-08-19T17:23:50Z
http://ijgt.ui.ac.ir/?_action=export&rf=summon&issue=4094
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
On nonsolvable groups whose prime degree graphs have four vertices and one triangle
Roghayeh
Hafezieh
Let $G$ be a finite group. The prime degree graph of $G$, denoted by $Delta(G)$, is an undirected graph whose vertex set is $rho(G)$ and there is an edge between two distinct primes $p$ and $q$ if and only if $pq$ divides some irreducible character degree of $G$. In general, it seems that the prime graphs contain many edges and thus they should have many triangles, so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles. In this paper we consider the case where for a nonsolvable group $G$, $Delta(G)$ is a connected graph which has only one triangle and four vertices.
prime degree graph
irreducible character degree
triangle
2018
09
01
1
6
http://ijgt.ui.ac.ir/article_21476_7aa9bd067cc2235a1faa46dd8f4728af.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
Groups with permutability conditions for subgroups of infinite rank
Anna Valentina
De Luca
Roberto
Ialenti
In this paper, the structure of non-periodic generalized radical groups of infinite rank whose subgroups of infinite rank satisfy a suitable permutability condition is investigated.
Group of infinite rank
almost permutable subgroup
nearly permutable subgroup
2018
09
01
7
16
http://ijgt.ui.ac.ir/article_21483_4b600a56b8f0ea252f47e0a58de19bf7.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
Inertial properties in groups
Ulderico
Dardano
Dikran
Dikranjan
Silvana
Rinauro
Let $G$ be a group and $p$ be an endomorphism of $G$. A subgroup $H$ of $G$ is called $p$-inert if $H^pcap H$ has finite index in the image $H^p$. The subgroups that are $p$-inert for all inner automorphisms of $G$ are widely known and studied in the literature, under the name inert subgroups. The related notion of inertial endomorphism, namely an endomorphism $p$ such that all subgroups of $G$ are $p$-inert, was introduced in cite{DR1} and thoroughly studied in cite{DR2,DR4}. The ``dual" notion of fully inert subgroup, namely a subgroup that is $p$-inert for all endomorphisms of an abelian group $A$, was introduced in cite{DGSV} and further studied in cite{Ch+, DSZ,GSZ}. The goal of this paper is to give an overview of up-to-date known results, as well as some new ones, and show how some applications of the concept of inert subgroup fit in the same picture even if they arise in different areas of algebra. We survey on classical and recent results on groups whose inner automorphisms are inertial. Moreover, we show how inert subgroups naturally appear in the realm of locally compact topological groups or locally linearly compact topological vector spaces, and can be helpful for the computation of the algebraic entropy of continuous endomorphisms.
commensurable
inert
inertial endomorphism
entropy
intrinsic entropy
scale function
growth
locally compact group
locally linearly compact space
Mahler measure
Lehmer problem
2018
09
01
17
62
http://ijgt.ui.ac.ir/article_21611_00d5ab9d6cd65813b0631a40fa7db9fb.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
Finite groups with non-trivial intersections of kernels of all but one irreducible characters
Mariagrazia
Bianchi
Marcel
Herzog
In this paper we consider finite groups $G$ satisfying the following condition: $G$ has two columns in its character table which differ by exactly one entry. It turns out that such groups exist and they are exactly the finite groups with a non-trivial intersection of the kernels of all but one irreducible characters or, equivalently, finite groups with an irreducible character vanishing on all but two conjugacy classes. We investigate such groups and in particular we characterize their subclass, which properly contains all finite groups with non-linear characters of distinct degrees, which were characterized by Berkovich, Chillag and Herzog in 1992.
Finite groups
Complex characters
2018
09
01
63
80
http://ijgt.ui.ac.ir/article_21609_42a17a94ecfbfa1359519bb03978b0aa.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
On some integral representations of groups and global irreducibility.
Dmitry
Malinin
Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let $K$ be a finite extension of the rational number field and $O_K$ the ring of integers of $K$. Let $G$ be a finite subgroup of $GL(2,K)$, the group of $(2 times 2)$-matrices over $K$. We obtain some conditions on $K$ for $G$ to be conjugate to a subgroup of $GL(2,O_K)$.
globally irreducible representations
class numbers
genera
Hilbert symbol
torsion points of elliptic curves
2018
09
01
81
94
http://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf
International Journal of Group Theory
Int. J. Group Theory
2251-7650
2251-7650
2018
7
3
Fragile words and Cayley type transducers
Daniele
D'Angeli
Emanuele
Rodaro
We address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties that we call fragile words. By using this notion, we exhibit a series of transducers constructed from Cayley graphs of finite groups whose defined semigroups are free, and thus having exponential growth.
Fragile words
Cayley type transducers
automaton groups
2018
09
01
95
109
http://ijgt.ui.ac.ir/article_21976_d42f2c0b8452fc83cb7f694995548600.pdf