Results 41 to 50 of about 203 (134)
The intersection of Sylow subgroups [PDF]
Proceedings of the American Mathematical Society, 1975 Let G G be a finite soluble group. If the order of
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On the intersections of nilpotent subgroups in simple groups
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract Let G$G$ be a finite group and let Hp$H_p$ be a Sylow p$p$‐subgroup of G$G$. A recent conjecture of Lisi and Sabatini asserts the existence of an element x∈G$x \in G$ such that Hp∩Hpx$H_p \cap H_p^x$ is inclusion‐minimal in the set {Hp∩Hpg:g∈G}$\lbrace H_p \cap H_p^g \,:\, g \in G\rbrace$ for every prime p$p$.
Timothy C. Burness, Hong Yi Huang
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Derangements in intransitive groups
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract Let G$G$ be a nontrivial permutation group of degree n$n$. If G$G$ is transitive, then a theorem of Jordan states that G$G$ has a derangement. Equivalently, a finite group is never the union of conjugates of a proper subgroup. If G$G$ is intransitive, then G$G$ may fail to have a derangement, and this can happen even if G$G$ has only two ...
David Ellis, Scott Harper
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Linear characters of Sylow subgroups
Journal of Algebra, 2003 In this paper, the author was motivated by considering the McKay conjecture for finite groups with a self-normalizing Sylow \(p\)-subgroup. If \(p\geq 5\), the author clarifies the situation. Here are a few of the results in the paper: Theorem A.
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Alperin's bound and normal Sylow subgroups
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract Let G$G$ be a finite group, p$p$ a prime number and P$P$ a Sylow p$p$‐subgroup of G$G$. Recently, Malle, Navarro, and Tiep conjectured that the number of p$p$‐Brauer characters of G$G$ coincides with that of the normalizer NG(P)${\bf N}_G(P)$ if and only if P$P$ is normal in G$G$.
Zhicheng Feng +2 more
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Groups in which Sylow subgroups and subnormal subgroups permute
Illinois Journal of Mathematics, 2003 A finite group is called a PST-group if its subnormal subgroups permute with its Sylow subgroups. It is shown that if \(G\) is a PST-group and \(H_1/K_1\) and \(H_2/K_2\) are isomorphic Abelian chief factors of \(G\) with \(H_1H_2\subseteq G'\), then these factors are \(G\)-isomorphic (Theorem 2).
Ballester-Bolinches, A. +2 more
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The first two group theory papers of Philip Hall
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this paper, we discuss the first two papers on soluble groups written by Philip Hall and their influence on the study of finite groups. The papers appeared in 1928 and 1937 in the Journal of the London Mathematical Society.
Inna Capdeboscq
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Cyclotomic Classes in a Product of Finite Abelian Groups and Applications
Journal of Mathematics, Volume 2026, Issue 1, 2026.Cyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications. They naturally arise in diverse areas of mathematics, ranging from number theory and polynomial factorization to the decomposition of group ...
Somphong Jitman, Faranak Farshadifar
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Incorporating £‐Complex Intuitionistic Fuzzy Set to Sylow Theorems in Group Theory
Journal of Mathematics, Volume 2026, Issue 1, 2026.The complex intuitionistic fuzzy (CIF) set is an advanced version of the regular intuitionistic fuzzy set. It is made to better show the uncertainty and complexity that arise in real‐life problems. The grading and nongrading degrees in the CIF set are shown by complex‐valued functions that are defined on the unit disc of the complex plane.
Muhammad Jawad +5 more
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Strongly Base-Two Groups. [PDF]
Vietnam J Math, 2023 Burness TC, Guralnick RM.
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