McLain's group is a particular kind of unitriangular matrix group of infinite degree over a ring. Specifically, for a ring and a partially ordered indexing set , define:
as the group of automorphisms of generated by the elementary matrices:
McLain's group over a ring is defined as the group , where is the set of rational numbers with its usual total ordering.
McLain's group is denoted or sometimes simply . It is typically considered in cases where is a field or division ring. Both the characteristic zero case (e.g., ) and the characteristic case (e.g., ) generate groups of interest.
|Book||Page number||Chapter and section||Contextual information||View|
|A Course in the Theory of Groups by Derek J. S. Robinson, ISBN 0387944613More info||348||Section 12.1||formal definition introduced as 12.1.9||Google Books|
- MathOverflow question: A question about matrices: The questions asks for details on McLain's group. Person asking the question is unable to access the original McLain paper with the details