Zassenhaus Conjecture (ZC1) on torsion units of integral group rings for some metabelian groups
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چکیده
منابع مشابه
On the first Zassenhaus conjecture for integral group rings
It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring of a finite group is conjugate to a group element within the rational group algebra. The object of this note is the computational aspect of a method developed by I. S. Luthar and I. B. S. Passi which sometimes permits an answer to this conjecture. We illustrate the method on certain explicit examples. We prove wit...
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It is shown that any torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture ho...
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Suppose that a group G has a normal subgroup C where C and G/C are cyclic of relatively prime orders. Then any torsion unit in ZG is rationally conjugate to a trivial unit.
متن کاملTorsion units in integral group rings of Janko simple groups
Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.
متن کاملTorsion Units in Integral Group Rings of Conway Simple Groups
Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2006
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-005-1554-0