## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 44, Number 3 (2014), 341-350.

### Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’

José María Montesinos-Amilibia

#### Abstract

Cassels proved that projectively equivalent integral quadratic forms are
commensurable. In this note, an elementary proof of the converse of this theorem,
for indefinite forms, is given. This was proved in "On integral quadratic forms having commensurable groups of
automorphisms," *Hiroshima Math. J.* 43, 371–411 (2013) for forms of Sylvester signature
+++. . .+- or ---. . .-+ (hyperbolic forms) and it was left there, as an open
problem, for non-hyperbolic indefinite forms of any Sylvester signature.

#### Article information

**Source**

Hiroshima Math. J., Volume 44, Number 3 (2014), 341-350.

**Dates**

First available in Project Euclid: 26 December 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1419619751

**Digital Object Identifier**

doi:10.32917/hmj/1419619751

**Mathematical Reviews number (MathSciNet)**

MR3296080

**Zentralblatt MATH identifier**

1315.11023

**Subjects**

Primary: 11E04: Quadratic forms over general fields 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions

**Keywords**

Integral quadratic form automorph commensurability class

#### Citation

Montesinos-Amilibia, José María. Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’. Hiroshima Math. J. 44 (2014), no. 3, 341--350. doi:10.32917/hmj/1419619751. https://projecteuclid.org/euclid.hmj/1419619751

#### See also

- See: José María Montesinos-Amilibia. On integral quadratic forms having commensurable groups of automorphisms. Hiroshima Math. J., vol. 43, no. 3 (2013), pp. 371-411.Project Euclid: euclid.hmj/1389102581