Intersections of prefrattini subgroups in finite soluble groups
Sergey
Kamornikov
Gomel Branch of International University MITSO
author
text
article
2017
eng
Let $H$ be a prefrattini subgroup of a soluble finite group $G$. In the paper it is proved that there exist elements $x,y \in G$ such that the equality $H \cap H^x \cap H^y = \Phi (G)$ holds.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
2
no.
2017
1
5
http://ijgt.ui.ac.ir/article_11163_3650d54fe69af739215f4d9e4faf6065.pdf
dx.doi.org/10.22108/ijgt.2017.11163
Nonnilpotent subsets in the Suzuki groups
Mohammad
Zarrin
University of Kurdistan
author
text
article
2017
eng
Let $G$ be a group and $\mathcal{N}$ be the class of all nilpotent groups. A subset $A$ of $G$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $A$, $\langle a, b\rangle \not\in \mathcal{N}$. If, for any other nonnilpotent subset $B$ in $G$, $|A|\geq |B|$, then $A$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $\omega(\mathcal{N}_G)$. In this paper, among other results, we obtain $\omega(\mathcal{N}_{Suz(q)})$ and $\omega(\mathcal{N}_{PGL(2,q)})$, where $Suz(q)$ is the Suzuki simple group over the field with $q$ elements and $PGL(2,q)$ is the projective general linear group of degree $2$ over the finite field with $q$ elements, respectively.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
2
no.
2017
7
15
http://ijgt.ui.ac.ir/article_11176_3a4049d20a5e0a7916fa9b1738b69f83.pdf
dx.doi.org/10.22108/ijgt.2017.11176
A note on finite groups with the indice of some maximal subgroups being primes
Cui
Zhang
Yantai University
author
text
article
2017
eng
The Theorem 12 in [A note on $p$-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indices. In this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index are solvable.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
2
no.
2017
17
20
http://ijgt.ui.ac.ir/article_12396_c6588acf55ed792ee5a449031ab6b69a.pdf
dx.doi.org/10.22108/ijgt.2017.12396
Induced operators on symmetry classes of polynomials
Mahin
Ranjbari
Sahand University of Technology
author
Yousef
Zamani
Sahand University of Technology
author
text
article
2017
eng
In this paper, we give a necessary and sufficient condition for the equality of two symmetrized decomposable polynomials. Then, we study some algebraic and geometric properties of the induced operators over symmetry classes of polynomials in the case of linear characters.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
2
no.
2017
21
35
http://ijgt.ui.ac.ir/article_12406_fdb932fe750916f2cd3866200ac96347.pdf
dx.doi.org/10.22108/ijgt.2017.12406
Converse of Lagrange's theorem (CLT) numbers under $1000$
Jean B.
Nganou
University of Oregon
author
text
article
2017
eng
A positive integer $n$ is called a CLT number if every group of order $n$ satisfies the converse of Lagrange's Theorem. In this note, we find all CLT and supersolvable numbers up to $1000$. We also formulate some questions about the distribution of these numbers.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
2
no.
2017
37
42
http://ijgt.ui.ac.ir/article_13314_188efd7436d4971e7d2e54f372a19e7a.pdf
dx.doi.org/10.22108/ijgt.2017.13314