## Bulletin of the Australian Mathematical Society

### On tensor factorisation for representations of finite groups

a1 Dipartimento di Matematica ‘Ulisse Dini’, Università degli Studi di Firenze, viale Morgagni 67-A, 50134 Firenze, Italy, e-mail: pacifici@math.unifi.it

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.