Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414726 | Journal of Algebra | 2014 | 18 Pages |
Abstract
An element g of a group is called reversible if it is conjugate in the group to its inverse. An element is an involution if it is equal to its inverse. This paper is about factoring elements as products of reversibles in the group Gn of formal maps of (Cn,0), i.e. formally-invertible n-tuples of formal power series in n variables, with complex coefficients. The case n=1 was already understood [25].Each product F of reversibles has linear part L(F) of determinant ±1. The main results are that for n⩾2 each map F with det(L(F))=±1 is the product of 2+3â ceiling(log2n) reversibles, and may also be factored as the product of 9+6â ceiling(log2n) involutions (where the ceiling of x is the smallest integer ⩾x).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anthony G. OʼFarrell, Dmitri Zaitsev,