International Journal of Group Theory
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ارسال های اخیر
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Harada's conjecture II for the finite general linear groups and unitary groups
(University of Isfahan, 2025-12-01)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 ...
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Notes on influence of certain permutable subgroups on finite smooth groups
(University of Isfahan, 2025-12-01)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 ...
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Exponential and weakly exponential subgroups of finite groups
(University of Isfahan, 2025-12-01)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 ...
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Lifting automorphisms of subgroups of direct products of cyclic $p$-groups
(University of Isfahan, 2025-12-01)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 ...
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The probability that two elements of a group have the same centralizers
(University of Isfahan, 2025-12-01)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 ...
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Quantitative characterization of finite simple groups: a complement
(University of Isfahan, 2025-12-01)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 ...
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$p$-groups with a small number of character degrees and their normal subgroups
(University of Isfahan, 2025-09-01)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 ...
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Groups whose same-order types are arithmetic progressions
(University of Isfahan, 2025-09-01)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 ...
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On a question of Jaikin-Zapirain about the average order elements of finite groups
(University of Isfahan, 2025-09-01)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 ...
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Representation theory of skew braces
(University of Isfahan, 2025-09-01)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 ...
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Cartesian symmetry classes associated with certain subgroups of $S_m$
(University of Isfahan, 2025-09-01)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 ...
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A characterization of $A_5$ by its average order
(University of Isfahan, 2025-09-01)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 ...
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Group nilpotency from a graph point of view
(University of Isfahan, 2024-12-01)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 ...
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A study on the structure of finite groups with $c$-subnormal subgroups
(University of Isfahan, 2024-12-01)In this paper, we use the definition of the concept ``c-Subnormal Subgroup" to study the structure of a given finite group $G$ which contains some $c-$subnormal subgroups. We prove two main theorems, which answer the ...
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A lattice theoretic characterization for the existence of a faithful irreducible representation
(University of Isfahan, 2024-12-01)In a recent article S\'ebastien Palcoux formulated a sufficient condition on the subgroup lattice of a finite group $G$ that guarantees the existence of a faithful irreducible complex representation of $G$, and asked whether ...
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Determination of the left braces of order $64$
(University of Isfahan, 2024-12-01)We review some of the algorithms used for the determination of the left braces of order $64$.
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Generalized nilpotent braces and nilpotent groups
(University of Isfahan, 2025-03-01)The authors give a brief survey of some results concerning nilpotent braces and their generalizations. Various results concerning $\star$-hypercentral and locally $\star$-nilpotent braces are given.
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On groups with many normal subgroups
(University of Isfahan, 2025-03-01)The structure of groups which are rich in normal subgroups has been investigated by several authors. Here, we prove that if a radical group G has normal deviation, which means that the set of its non-normal subgroups ...
