Realization of even permutations of even degree by products of four involutions without fixed points.

We consider representations of an arbitrary permutation π of degree 2n, n ⩾ 3, by products of the so-called (2n)-permutations (any cycle of such a permutation has length 2). We show that any even permutation is represented by the product of four (2n)-permutations. Products of three (2n)-permutations cannot represent all even permutations. Any odd permutation is realized (for odd n) by a product of five (2n)-permutations. [ABSTRACT FROM AUTHOR]