abstract We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.

Abstract Let $${\mathbb {K}}={\mathbb {R}},\,{\mathbb {C}}$$ K = R , C , the field of reals or complex numbers and {H}}$$ H skew {R}}$$ -algebra quaternions. We study homotopy nilpotency ...

Article history: Received 13 May 2010 Accepted 1 June 2010 Available online 4 July 2010 Submitted by R.A. Brualdi AMS classification: 15A15 15A18

Conditions are given for a class 2 nilpotent group to have no central extensions of class 3. This is related to Betti numbers and to the problem of representing a class 2 nilpotent group as the fundamental group of a smooth projective variety. Surveys of the work on the characterization of the fundamental groups of smooth projective varieties and Kähler manifolds (see [1],[3], [9]) indicate tha...

We build presentations for automata groups generated by Cayley machines of finite nilpotency class two and prove that these are all cross-wired lamplighter groups.

Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.