We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 ...

Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a ...

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm ...

Verlinde conjectured that gravitation is an emergent entropic force. This surprising conjecture was proved in Plastino and Rocca (2018) within a purely classical context. Here, we appeal to a quantum environment to deal ...

For any given subgroup H of a finite group G, the Quillen poset of nontrivial elementary abelian p-subgroups is obtained from by attaching elements via their centralisers in H. We exploit this idea to study Quillen's ...

We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that B > 15, where B is the minimum of the greatest common divisor of the total degrees of P and Q , where ( P , Q ) ...