Higman

In mathematics, "Higman" can refer to several concepts associated with the mathematician Graham Higman. These include:

• Higman's Embedding Theorem: A significant result in group theory stating that every finitely generated group can be embedded as a subgroup of a finitely presented group if and only if it can be embedded in a finitely presented group. This theorem has important implications for the study of finitely generated groups and their representations. The finitely presented group constructed in the theorem's proof is often referred to as a Higman group.

• Higman's Linearly Ordered Group Theorem: Also within group theory, this theorem states conditions under which an ordered group can be embedded into another ordered group with certain properties.

• Higman's Lemma: A result in combinatorics and order theory dealing with well-quasi-orders. It states that for any infinite sequence of words over a finite alphabet, there exist two words in the sequence such that the first is an infixed subword of the second. This has applications in computer science, particularly in termination proofs of term rewriting systems.

• Higman Groups: This term may refer generally to groups constructed using techniques pioneered by Graham Higman, often characterized by specific presentations or properties relating to embedding theorems.

Understanding the context is crucial when encountering the term "Higman" to determine the specific mathematical concept being referenced.