In a previous work of the authors, a middle convolution operation on the category of Fuchsian differential systems was introduced. In this note we show that the middle convolution of Fuchsian systems preserves the property of global nilpotence. This leads to a globally nilpotent Fuchsian system of rank two which does not belong to the known classes of globally nilpotent rank two systems. Moreov...

Abstract We investigate the topological nilpotence degree, in sense of Henn–Lannes–Schwartz, a connected Noetherian unstable algebra R . When is mod p cohomology ring compact Lie group, Kuhn showed how this invariant controlled by centralizers elementary abelian -subgroups. By replacing -subgroups with components Lannes’ T -functor, and utilizing techniques algebras over Steenrod algebra, we ar...

For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M ]. This strengthens the K2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any regular ring and the stableK2-group is substituted by the unstable ones. The proof is based on a polyhedral/combinatorial techniques, computations...

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |XXX|/|X| bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of G. We also find a connection with Lie groups, and use it to obtain some consequences s...

Abstract Residual torsion-free nilpotence has proved to be an important property for knot groups with applications bi-orderability and ribbon concordance. Mayland proposed a strategy show that two-bridge group commutator subgroup which is union of ascending chain para-free groups. This paper proves Mayland’s assertion expands the result subgroups link correspond kernels maps $\mathbb{Z}$ . We c...