Zassenhaus

Zassenhaus is a surname most prominently associated with Hans Zassenhaus, a German-born mathematician who later worked in the United States. His research spanned group theory, Lie algebras, and computational algebra, and several results bear his name.

In pure mathematics, the Zassenhaus lemma (also known as the butterfly lemma) is a classical result about the arrangement of subgroups and their factor groups within a group; it is a key tool in the study of subgroup lattices and in proving other isomorphism theorems.

In Lie theory, the Zassenhaus formula describes a product decomposition for the exponential of a sum of noncommuting elements, expressing exp(X+Y) as a product of exponentials of nested commutators. It is used in the analysis of Lie algebras and in related computations.

In computational algebra, the Zassenhaus algorithm (or Zassenhaus factoring method) is a method for factoring polynomials over finite fields; the algorithm lifts factors modulo primes to factors over the polynomial ring and is implemented in many computer algebra systems.

The surname Zassenhaus thus identifies a suite of foundational ideas in algebra and its applications, reflecting Hans Zassenhaus’s influence across theory and computation.