Transposition invariant words
We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n and primitive roots. In particular, we show that there are infinitely many prime numbers p with a primitive root dividing p + 1 and infinitely many prime numbers p without a primitive root dividing p + 1. We also consider the orbit of a word under transposition. (c) 2007 Elsevier B.V. All rights reserved.
transposition invariant words primitive roots partition generated by a subgroup favorable prime numbers