On the torsion of the group image of integral Lorentzian (n + 1) × (n + 1) matrices Original Research Article

In this paper, we investigate the torsion of the group image of integral Lorentzian (n + 1) × (n + 1) matrices. We show that for any odd prime number p, the group image has an element of order p if and only if n ≥ p or n + 1 = p ≡ 1 mod 4. We determine the maximal order of a p-subgroup of image for certain prime numbers p. In particular, we prove that if p is a regular prime number such that p ≡ 1 mod 4 and if pa is the maximal order of a p-subgroup of image, then image, where square brackets denotes the greatest integer function. We also determine the maximal order of a p-subgroup of image for each prime number p for n = 1, …, 42.