310 hasil
Menampilkan 1–20 · 0,39 detik · RSS
International Journal of Group Theory
Scopus
ISSN 2251-7650 · University of Isfahan · 310 artikel di indeks
-
Artikel Jurnal Teks lengkap
On numbers which are orders of nilpotent groups with bounded class
Let $n$ be a positive integer. In this short note, we characterize those numbers $m$ for which any group of order $m$ is an $n$-Engel group and those numbers $m$ for which any group of order $m$ has all its subgroups subnormal of defect at most $n$.
-
Artikel Jurnal Teks lengkap
Harada's conjecture II for the finite general linear groups and unitary groups
K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the…
-
Artikel Jurnal Teks lengkap
Notes on influence of certain permutable subgroups on finite smooth groups
A maximal chain of a finite group $G$ is called smooth if any two intervals have the same length are isomorphic. A group $G$ is called totally smooth if all maximal chains of $G$ are smooth, and called generalized smooth if all chains from each subgroup of prime order to $G$ are smooth. In the…
-
Artikel Jurnal Teks lengkap
Exponential and weakly exponential subgroups of finite groups
Sabatini [L. Sabatini, Products of subgroups, subnormality, and relative orders of elements, Ars Math. Contemp., 24 no. 1 (2024) 9 pp.] defined a subgroup $H$ of $G$ to be an exponential subgroup if $x^{|G:H|} \in H$ for all $x \in G$, in which case we write H ≤exp G. Exponential subgroups are a…
-
Artikel Jurnal Teks lengkap
Quantitative characterization of finite simple groups: a complement
In this paper, we summarize the research on the characterization of finite simple groups and the study of finite groups based on their ``set of element orders" and ``two orders" (the order of the group and the set of element orders). We also discuss some related topics, their applications, and…
-
Artikel Jurnal Teks lengkap
The probability that two elements of a group have the same centralizers
In this paper we provide some bounds for the probability, denoted by $\mathcal{PC}(G)$, that two randomly chosen elements in a given finite group have the same centralizers. In particular, among other results, we give the following best possible bounds for $\mathcal{PC}(G)$, depending only on…
-
Artikel Jurnal Teks lengkap
Lifting automorphisms of subgroups of direct products of cyclic $p$-groups
Let $\Gamma$ be a finite group. A subgroup $H$ of $\Gamma$ is called ``fully liftable" in $\Gamma$ if every automorphism of $H$ is the restriction of an automorphism of $\Gamma$. Let $G=C_{p^{k_1}}\times C_{p^{k_2}}$, where $1\le k_1\le k_2$ and $p$ is prime. Using information about the subgroup…
-
Artikel Jurnal Teks lengkap
A characterization of $A_5$ by its average order
Let $o(G)$ be the average order of a finite group $G$. M. Herzog, P. Longobardi and M. Maj [M. Herzog, P. Longobardi and M. Maj, Another criterion for solvability of finite groups, J. Algebra, 597 (2022) 1-23.] showed that if $G$ is non-solvable and $o(G)=o(A_5)$, then $G\cong A_5$. In this note…
-
Artikel Jurnal Teks lengkap
Groups whose same-order types are arithmetic progressions
For any group $G$, define $g\sim h$ if $g,h\in G$ have the same order. The set of sizes of the equivalent classes with respect to this relation is called the same-order type of $G$. In this short note we prove that there is no finite group whose same-order type is an arithmetic progression of…
-
Artikel Jurnal Teks lengkap
Cartesian symmetry classes associated with certain subgroups of $S_m$
In this paper, the problem existing $O$-basis for Cartesian symmetry classes is discussed. The dimensions of Cartesian symmetry classes associated with a cyclic subgroup of the symmetric group $S_m$ (generated by a product of disjoint cycles) and the product of cyclic subgroups of $S_m$ are…
-
Artikel Jurnal Teks lengkap
On a question of Jaikin-Zapirain about the average order elements of finite groups
For a finite group $G$, the average order $o(G)$ is defined to be the average of all order elements in $G$, that is $o( G)=\frac{1}{|G|}\sum_{x\in G}o(x)$, where $o(x)$ is the order of element $x$ in $G$. Jaikin-Zapirain in [On the number of conjugacy classes of finite nilpotent groups, Advances in…
-
Artikel Jurnal Teks lengkap
On some groups whose subnormal subgroups are contranormal-free
If $G$ is a group, a subgroup $H$ of $G$ is said to be contranormal in $G$ if $H^G = G$, where $H^G$ is the normal closure of $H$ in $G$. We say that a group is contranormal-free if it does not contain proper contranormal subgroups. Obviously, a nilpotent group is contranormal-free. Conversely, if…
-
Artikel Jurnal Teks lengkap
$p$-groups with a small number of character degrees and their normal subgroups
If $G$ be a finite $p$-group and $\chi$ is a non-linear irreducible character of $G$, then $\chi(1)\leq |G/Z(G)|^{\frac{1}{2}}$. In \cite{fernandez2001groups}, Fern\'{a}ndez-Alcober and Moret\'{o} obtained the relation between the character degree set of a finite $p$-group $G$ and its normal…
-
Artikel Jurnal Teks lengkap
Representation theory of skew braces
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility condition. Following their definition, we shall explain how some…
-
Artikel Jurnal Teks lengkap
On groups satisfying the double chain condition on nonascendant subgroups
If $\theta$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\theta$-subgroups if it admits no infinite double chain $$\cdots
-
Artikel Jurnal Teks lengkap
Group nilpotency from a graph point of view
Let $\Gamma_G$ denote a graph associated with a group $G$. A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $\Gamma_H$ is isomorphic to $\Gamma_G$ for a finite nilpotent group $G$. In the present work we analyze the problem for different…
-
Artikel Jurnal Teks lengkap
Finite coverings of semigroups and related structures
For a semigroup $S$, the covering number of $S$ with respect to semigroups, $\sigma_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$. This article investigates covering numbers of semigroups and analogously defined covering numbers of inverse semigroups and monoids…
-
Artikel Jurnal Teks lengkap
Advances on a construction related to the non-abelian tensor square of a group
This is a survey on a group construction in connection with the non-abelian tensor square of groups. We report on the developments obtained in the last decade emphasizing the results from a commutator point of view.
-
Artikel Jurnal Teks lengkap
New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups
In this survey we shall describe some recent criteria for solvability, nilpotency and other properties of finite groups $G$, based either on the orders of the elements of $G$ or on the orders of the subgroups of $G$.
-
Artikel Jurnal Teks lengkap
Remark on Laquer's theorem for circulant determinants
Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of Laquer's theorem. Also, we give an…