Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the Zassenhaus Conjecture for certain cyclic-by-nilpotent groups (1811.11554v3)

Published 28 Nov 2018 in math.GR

Abstract: Hans Zassenhaus conjectured that every torsion unit of the integral group ring of a finite group $G$ is conjugate within the rational group algebra to an element of the form $\pm g$ with $g\in G$. This conjecture has been disproved recently for metabelian groups, by Eisele and Margolis. However it is known to be true for many classes of solvable groups, as for example nilpotent groups, cyclic-by-abelian groups and groups having a cyclic Sylow subgroup with abelian complement. On the other hand, it is not known whether the conjecture holds for supersolvable groups. This paper is a contribution to this question. More precisely, we study the conjecture for the class of cyclic-by-nilpotent groups with special attention to the class of cyclic-by-Hamiltonian groups. We prove the conjecture for cyclic-by-$p$-groups and for a large class of cyclic-by-Hamiltonian groups.

Summary

We haven't generated a summary for this paper yet.