Using the Luthar-Passi method, we investigate the classical Zassen-haus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J 1 , J 2 and J 3 we confirm Kimmerle's conjecture on prime graphs.
Constructions are given of Noetherian maximal orders that are finitely presented algebras over a field K, defined by monomial relations. In order to do this, it is shown that the underlying homogeneous information determines the algebraic structure of the algebra. So, it is natural to consider such algebras as semigroup algebras K[S] and to investigate the… (More)
Let A be a finitely generated commutative algebra over a field K with terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relations. Also the class group of such algebras A is calculated.