Vol. 40, No. 2, 1972

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Uniform finite generation of the affine group

Franklin Lowenthal

Vol. 40 (1972), No. 2, 341–348

A connected Lie group H is said to be uniformly finitely generated by a given pair of one-parameter subgroups if there exists a positive integer n such that every element of H can be written as a finite product of length at most n of elements chosen alternately from the two one-parameter subgroups. Define the order of generation of H as the least such n. It is shown that the order of generation of the affine group is either 4 or 5 while its connected Lie subgroups (with two exceptions) have order of generation equal to their dimension.

Mathematical Subject Classification 2000
Primary: 22E10
Received: 30 September 1970
Published: 1 February 1972
Franklin Lowenthal