IJPAM: Volume 41, No. 4 (2007)
GROUPS INTO A PRODUCT OF INVOLUTIONS
Department of Mathematics
1-1 Keyakidai, Sakado, Saitama, 350-0295, JAPAN
Abstract.An element in an algebraic system is called an involution if . Our interest is to factorize elements in various algebraic systems into a product of as small number of involutions as possible.
In this direction we present Djocovic's two involution theorem for linear automorphisms, which he proved by using elementary divisors, whereas we will do it by using system of invariants of a finitely generated module over a principal ideal domain. As a result the proof will become rather simpler.
Also we shall introduce without proof some results on factorizations of elements in some
classical groups into a product of involutions.
Received: September 28, 2007
AMS Subject Classification: 15A04, 15A23, 15A33
Key Words and Phrases: involution, structure theorem of modules over PID, factorization of linear maps and matrices
Source: International Journal of Pure and Applied Mathematics