We call (1) a central series of G of length n. The minimal length of a central series is called the nilpotency class of G. For example, an abelian group is nilpotent with nilpotency class · 1. Some …

Definition 5.1.1 A Lie algebra is called nilpotent if there exists a decreasing finite sequence (gi)i∈[0,k] of ideals such that g0 = g, gk = 0 and [g, gi] ⊂ gi+1 for all i ∈ [0, k − 1].

Introduction NILPOTENT POLYNOMIALS AND NILPOTENT COEFFICIENTS JANEZ ˇS f Nil(R)[x]. In this paper we give an example in the converse direction: f Nil(R[x]). This is achieved by ying f2 = 0. …

The unitriangular groups UTN(Z) are nilpotent because addition is additive on the first nonzero superdiagonal, so taking nested commutators will terminate in at most N-1 steps

Nilpotent elements have interesting properties and applications in algebraic geometry, algebraic topology and representation theory. In this essay, we will explore the concept of nilpotent elements in …

The properties of nilpotent group given in Theorem 24.14 are analogous to the first two properties of solvable groups from Theorem 23.6. The third part of that theorem (if H, G/H are solvable then so is …

The following theorem is the nilpotent analogue of Lie’s Theorem (Theorem 4.2.3). While Lie’s Theorem only holds for complex vector spaces, the theorem below holds for F = R or C.