The B B Newman spelling theorem

Abstract

This article aims to be a self-contained account of the history of the B B Newman Spelling Theorem, including the historical context in which it arose. First, an account of B B Newman and how he came to prove his Spelling Theorem is given, together with a description of the author's efforts to track this information down. Following this, a high-level description of combinatorial group theory is given. This is then tied in with a description of the history of the word problem, a fundamental problem in the area. After a description of some of the theory of one-relator groups, an important part of combinatorial group theory, the natural division line into the torsion and torsion-free case for such groups is described. This culminates in a statement of and general discussion about the B B Newman Spelling Theorem and its importance.