IJPAM: Volume 41, No. 4 (2007)

FACTORIZATION OF ELEMENTS IN CLASSICAL
GROUPS INTO A PRODUCT OF INVOLUTIONS

Hiroyuki Ishibashi
Department of Mathematics
Josai University
1-1 Keyakidai, Sakado, Saitama, 350-0295, JAPAN
e-mail: hishi@math.josai.ac.jp


Abstract.An element $\tau$ in an algebraic system is called an involution if $\tau^2 = 1$. 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
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4