Nilpotency of the pure spinor BRST operator in a curved background implies superspace equations of motion for the background. By computing one-loop corrections to nilpotency for the heterotic sigma model, the Yang-Mills Chern-Simons corrections to the background are derived.

It is known that strongly nilpotent matrices over a division ring are linearly triangularizable. We describe the structure of such matrices in terms of the strong nilpotency index. We apply our results on quasi-translation x+H such that JH has strong nilpotency index two.

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of GL(d,Q) and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of GL(d,Q).

Theoretical foundations of a new algorithm for determining the p-capitulation type K ( )  of a number field K with p-class rank = 2  are presented. Since K ( )  alone is insufficient for identifying the second p-class group p K K = 2 Gal(F | ) G of K, complementary techniques are developed for finding the nilpotency class and coclass of G . An implementation of the complete algorithm in the ...

Of course, in that problem we have to take into account that the class sizes impose restrictions on the group structure. E.g. if the sizes are {1, p}, then the nilpotency class has to be 2. More precisely: the class sizes of a p-group G are {1, p} iff |G′| = p (Knoche; see also Theorem 3 below). But we can ask, e.g., if, given any set S ≠ {1, p} of p-powers, does there exist a group of class 3 ...

Abstract Let G be a finite group and assume that of automorphisms A acts on , such the orders are relatively prime. We prove fact imposing certain conditions set maximal -invariant subgroups relating to nilpotency, p -nilpotency, normality or having p’ -order, determines properties structure as solubility, -solubility -nilpotency.