 
Summary: Permutation involvement and groups
M.D. Atkinson
Department of Computer Science
University of Otago
Dunedin, New Zealand
mike@cs.otago.ac.nz
Robert Beals
Department of Mathematics, University of Arizona
617 North Santa Rita, Tucson, Arizona 85721, USA
beals@math.arizona.edu
Abstract
Sets of permutations which are closed under both pattern involvement
and multiplication are classied.
Keywords Permutation, forbidden, restricted, group
1 Introduction
Over the last few years there has been much interest in both combinatorics
and computer science in the notion of permutation involvement. Although we
shall often use cycle notation for permutations, involvement is best described by
writing permutations in image form as a sequence [1 ; 2 ; : : : ]. We recall that
a permutation is involved in a permutation if, when written in image form,
