A counterexample to the first Zassenhaus conjecture
نویسندگان
چکیده
منابع مشابه
Another Counterexample to a Conjecture of Zassenhaus
A metabelian group G of order 1440 is constructed which provides a counterexample to a conjecture of Zassenhaus on automorphisms of integral group rings. The group is constructed in the spirit of [8]. An augmented automorphism of ZG which has no Zassenhaus factorization is given explicitly (this was already done in [7] for a group of order 6720), but this time only a few distinguished group rin...
متن کاملOn 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...
متن کاملZassenhaus Conjecture for A6
For the alternating group A6 of degree 6, Zassenhaus’ conjecture about rational conjugacy of torsion units in integral group rings is confirmed.
متن کاملA Counterexample to Borsuk's Conjecture
Let f(d) be the smallest number so that every set in Rd of diameter 1 can be partitioned into f(d) sets of diameter smaller than 1. Borsuk's conjecture was that f(d)=d+\ . We prove that f(d)>(\.2)^ for large d.
متن کاملA Counterexample to the Finite Height Conjecture
By J onsson's Lemma, the variety V(K) generated by a nite lattice has only nitely many subvarieties. This led to the conjecture that, conversely, if a lattice variety has only nitely many subvarieties, then it is generated by a nite lattice. A stronger form of the conjecture states that a nitely generated variety V(K) has only nitely many covers in the lattice of lattice varieties, and that eac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.10.004