Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question

DOI10.1515/forum-2022-0086OpenAlexW4319342977MaRDI QIDQ2689770

Andreas Bächle, Sugandha Maheshwary, Ann Kiefer, Ángel Del Río

Publication date: 14 March 2023

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.08188

zbMATH Keywords

group ringsgroups of unitsprime graphcut propertyGruenberg-Kegel graph

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (1)

The Gruenberg-Kegel graph of finite solvable rational groups

Uses Software

• GAP
• ATLAS Group Representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On finite groups with disconnected prime graph.
• A characterization of the prime graphs of solvable groups.
• Frobenius \(\mathbb{Q}\)-groups.
• Integral group rings of solvable groups with trivial central units
• Group ring groups. Volume 1: Orders and generic constructions of units.
• On realizability of a graph as the prime graph of a finite group
• On finite rational groups and related topics
• On the prime graph of \(\text{PSL}(2,p)\) where \(p>3\) is a prime number.
• 2-Frobenius \(\mathbb{Q}\)-groups.
• Prime graph components of finite groups
• Groups whose characters are rational-valued
• Integral group rings with all central units trivial
• Non-abelian composition factors of finite groups with the CUT-property
• On the prime graph question for integral group rings of 4-primary groups. II.
• Integral group rings with all central units trivial: solvable groups
• Simple components and central units in group algebras.
• A counterexample to the first Zassenhaus conjecture
• A dichotomy for integral group rings via higher modular groups as amalgamated products
• Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph
• Global and local properties of finite groups with only finitely many central units in their integral group ring
• Field of values of cut groups and \(k\)-rational groups
• Finite simple groups with short Galois orbits on conjugacy classes
• On the realizability of a graph as the Gruenberg-Kegel graph of a finite group
• Recent advances on torsion subgroups of integral group rings
• CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p^k) WHERE p AND k > 1 ARE ODD
• Finite Groups in Which Every Element Has Prime Power Order
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
• PRIME GRAPH COMPONENTS OF FINITE SIMPLE GROUPS
• The Orders of Torsion Units in Integral Group Rings of Finite Solvable Groups
• Semi-rational solvable groups
• Decomposition of the Augmentation Ideal and of the Relation Modules of a Finite Group
• Integral Group Rings with Trivial Central Units
• The diameter of the prime graph of a finite group
• Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups
• On the Gruenberg–Kegel graph of integral group rings of finite groups
• On groups having the prime graph as alternating and symmetric groups
• Orders of units in integral group rings and blocks of defect 1
• On the prime graph of a finite group with unique nonabelian composition factor
• An application of blocks to torsion units in group rings
• ON THE PRIME GRAPH OF SIMPLE GROUPS
• Abelianization and fixed point properties of units in integral group rings

This page was built for publication: Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question