We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies given polynomial identity r(t) = 0. In the special case of r=tn−1 we obtain uniform bound on class periodic derivation order n. even find optimal in characteristic p if does not divide certain invariant ρn.

Let G be a finite group, p a fix prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.

We give methods for bounding the higher-order filling functions of a homogeneous nilpotent group and apply them to a family of quadratically presented groups constructed by S. Chen[9]. We find sharp bounds on some higher-order filling invariants of these groups. In particular, we show that groups with arbitrarily large nilpotency class can have euclidean n-dimensional filling volume and give an...

We review the detailed structure of the large N = 4 superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing N = 4 strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical N = 4 string theories. e-mail address: [email protected] e-mail address: [email protected], ohta@...

A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be equivalent to the nonexistence of oriented cycles in the graph. Besides, the automorphism group of any evolution algebra E with E = E will be shown to be al...

We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...